Pretty much any amount of superpowers at all will cause human history to be dramatically different from our timeline
The thing about history is it's a very complex subject where even the slightest change would produce massive divergences. Social, cultural and political trends are in large part driven by people's reactions to major (then-)current events, and our societies and laws are informed and influenced by what has happened before and what has worked and not worked. Even the smallest change would result in a massive butterfly effect that would warp everything around it. A world with superpowers, any degree of superpowers, should, realistically, not resemble the social and cultural landscape of the modern world at all.
Watchmen provides a pretty good example of this, where a social trend leading to an increase in non-powered costumed vigilantes and one outright superhuman is enough to cause massive changes in history and American culture, including widespread usage of clean energy-powered cars, Richard Nixon as a four-term president, and America winning the Vietnam War. This goes beyond someone who is as god-like as Doctor Manhattan. Even less-powerful superhumans would be enough to warp history to this degree (e.g., the X-Men Forge and Wolverine could potentially produce the same results with Vietnam and Lithium-powered cars).
In the real world, superhumans would also massively affect the political balance of power just by existing, simply because they represent an avenue of power that the politicians don't have universal control over. If the superhumans are natural and not part of an engineered arms race, the people running the status quo cannot dominate them the way they do financially and socially. In the real world, during the Cold War Russia would be terrified of the existence of Superman and the U.S. government would be rapidly scrabbling for contingencies because they know Superman won't obey the minute his definition of "the American way" differs from their own.
This goes beyond mere flying brick-level superhumans. Mad scientists and supergeniuses like Mr. Fantastic, Lex Luthor, or Mr. Freeze would rapidly have their technology available to the common person. Even if they didn't decide to simply sell it out of ideological reasons (I'm looking at you, Poison Ivy), governments would rapidly get their hands on their technology after they got arrested and start trying to re-engineer it to advance their own motives. This goes for alien invasions as well. Darkseid invades Earth and suddenly he's left Apokaliptan god-tech scattered all over the globe.
There would be many, many changes in history should there be any superpowers, anything stronger than, say, Daredevil. Even the existence of a group of people with powers similar to Luke Cage or Spider-Man would cause major historical ripples. Among the many changes, just to highlight a few major examples...
- World history should go very, very differently. Assuming superpowers occur due to random mutations or accidents of fate across the globe you would have a lot more cases where the presence of superhumans dramatically reshapes the world's political balance. Superpowers are basically a huge weapon of war and whoever has the best and most of them has the advantage. You'd get a lot more cases where a smaller country fights off a larger attacker due to the presence of superhumans as a force multiplier, so a lot of IRL historical invasions would fail (or alternatively, others would succeed).
- A good example of this? The Nazis, given how obsessed the Third Reich was with mysticism and alternate means to power and the fact that their invasion plans had low odds for long-term success due to a lack of materiel and natural resources for their war machine and the fact that they managed to aggravate almost everyone, including the USSR who massively outnumbered them. But if the Nazis had a disproportionate number of superhumans due to comic-book super-soldier programs, that might change how World War II ended up.
- Or consider what happens when a superhuman born in a developing nation gains an ability like, say, the ability to make crops bloom on command, generate clean water, or provide an unlimited source of clean energy. It would give that country a huge economic advantage.
- The presence of superpowers would also warp scientific history and discovery, as people become interested in why certain powers work and devote research along those lines. Or outright cause some inventions to be ignored (why invent powered flight when you have a class of people that flies?)
- Air power would become a bigger threat in military technology long before the invention of air superiority IRL if you have people that fly.
- Alternatively, if you had superpowers unequally distributed and disproportionately represented among a particular culture or ethnic group, that group would eventually come to dominate at the expense of all others. Superpowers for this culture would be like how guns and gunpowder allowed Europeans to run roughshod over cultures in the rest of the world. You would also have significant issues with Nazi-esque rhetoric where the group with superpowers would claim they are superior because only their group has all the powers.
- Christianity would probably not become the dominant religion in the West, and the same is true for Buddhism in the East. Jesus and Buddha's miracles cease to become interesting in the context of a world where powers or healing magic are commonplace. They might gain traction as powerful secular figures based on their rhetoric akin to how Judaism or Islam sees Jesus IRL, but they likely wouldn't achieve their current popularity. Without the spread of these populist, pro-social religions that support the little guy and present the idea that in the grand scheme of things everyone is cosmically equal (either through reincarnation in Buddhism or everyone being equal before God in Christianity), we probably wouldn't see the expansion of human rights. In particular, we would probably still have slavery around in the West, since the moral disconnect between Christian values and the institution of slavery was a huge issue for many pro-democracy politicians and one of the driving forces for the abolitionist movement. "Might makes right" social philosophies would be a lot more common.
- Europeans would have never colonized Africa, the Pacific, and the New World. Europeans mostly managed to colonize these parts of the globe (especially the New World) due to the use of firearms, iron armor, horses, and disease. The native populations often lacked this military advantage. Superpowers evens the playing field, especially given how small initial European expedition attempts were. Even if smallpox wiped out most of the native population, some native superhumans would survive and they would have wreaked havoc on the early European attempts at conquest and settlement. This is especially pertinent in the case of the Aztec and Inca empires. These empires, which had a population of 6 and 10 million people, respectably, would have had access to superhumans (and would have probably kept them at their capitals), and would have been able to smash Cortes and Pizarro's invasion attempts easily. The fact that these invasion attempts failed would probably cause European rulers to consider exploration of the New World a lost cause (the King of England almost wrote the New World off as not worh colonizing after Roanoke vanished and Jamestown was failing) and dissuade would-be conquistadors. E.g., Pizarro only attempted to overthrow the Inca after he saw how wealthy and powerful it made Cortes.
- Human sacrifice would probably be a lot more common. Studies of human social systems have found that human sacrifice tends to become more common in highly-stratified social systems where individual human life is devalued as a means of controlling the lower class. E.g., the Aztec empire, which depended heavily on manual labor for construction due to the lack of exploitable pack animals and hence people were more valuable as labor than as people, as well as having a stratified upper class. Create a society where society is stratified along biological lines due to superpowers and, well...
These changes would be much more prominent in earlier history than in more recent times. Today with modern technology and fire-arms someone like Spider-Man or Luke Cage wouldn't have that much of an influence. But to a Stone Age or Bronze Age culture like most pre-European New World cultures, ancient Greece, ancient Egypt, feudal Japan, etc., someone with Spider-Man or Luke Cage's powers would be like a living god. I mean, Luke Cage is basically modern day Achilles, and in The Iliad Achilles' presence basically dictates the course of the Trojan War.
Equality is Dead
A world with superpowers, especially flying brick and above powers, would also shoot ideas of equality under the law (isonomy) and liberalism in general stone dead. Society basically works because no individual is able to unilaterally apply their will over everyone else, even totalitarian dictators have to maintain the support of their inner circle, their generals, and the masses or else risk being overthrown. But what do you do when you have an individual whose power comes from themselves and cannot be stopped by mass action? Say a Superman-level superhuman gets convicted of a crime? How are you going to imprison someone who can't be held against their will and can easily escape from any normal prison? Or a superhuman dictator who can do whatever they like, enforcing whatever insane ideology they believe to be correct, simply because they are so powerful that no one can tell them "no" and they don't have to maintain the good will of the people? How do you deal with a society where some individuals really are physically "superior" to others to a degree that cannot be ignored in culture and law?
A good example of this can be seen in how the X-Men comics have treated the two cases where mutants created a sovereign mutant-run nation: Genosha and Krakoa. Genosha was ruled for a time by Magneto and the Brotherhood of Mutants, whereas currently in the comics Krakoa is ruled by a council of mutants that include Charles Xavier, Magneto, Apocalypse, Exodus, Mister Sinister, Mystique, Emma Frost, Sebastian Shaw, Jean Grey, Storm, and Cyclops. Note that in both cases it’s still the same Alpha and Omega-class mutants who are dictating policy to the rest, whereas the poor schmuck whose mutation merely consists of a tail or the ability to change color is still politically disenfranchised. The fact that the different degrees of mutant powers create a class system and a small group of people at the top are never really addressed in the comics. Nor the fact that this cabal of super-mutants basically gained political power by putting a metaphorical gun to the heads of the world's leaders to do what they say or else.
What this would end up doing is killing most of the humanistic movements of the Enlightement and the idea of universal human rights, since you have a group of people that are both biologically and socially not equal to other human beings, and that would frame how people would talk about what is the best or most moral system of social organization and governance. I don't think Karl Marx would be too happy about the existence of superhumans either, likely calling them "natural bourgeoise" or something and likely espousing Hitler-esque ideas on how they should all be destroyed since unlike the bourgeioise you cannot take their power away via social mechanisms or government-mandated seizure of their property, and hence they would perpetually be an uncontrollable threat to Marx' envisioned communist utopia. That is if Marx even comes up with the same ideas due to the existence of superhumans throwing a wrench into his ideals. That's potentially one of the most influential ideas in the last 150 years of human history being radically different or outright never proposed.
Destruction of Narratives
The presence of superpowers would also throw a huge wrench into historical narratives of group superiority or oppression. Namely because it makes no sense for a society to view a certain gender, sexuality, or ethnic group as inferior when those people can very easily be the most powerful. This is especially the case for women. For most of human history the majority of human societies have been heavily patriarchal and women have been seen as the "fairer sex". However, in a world with superpowers, assuming random distribution half of all superhumans would be women. Narratives of women being submissive, weaker, gentler, or "belonging in the home" would go flying out the window the minute some Roman or Chinese woman ripped apart an attacking force with her bare hands. Not to mention all the women that would use their powers to advance themselves socially and politically (Boudicca or Wu Zetian with laser eyes anyone?) Similar issues would be present with cases of sexual assault. Men would be hesitant to sexually assault women because they are now playing Russian roulette if they tried. Male superhuman sexual abuse cases would skyrocket, and female sexual assault and rape cases, which actually kind of common but brushed under the rug in current times, would become high profile as you now have women capable of easily overpowering men and having their way with them in an undismissable manner. Female superhumans might end up being stereotyped as promiscuous and sexually aggressive because of it.
Similarly, because superpowers are such a great weapon of war, it would be silly for a culture to sideline it's superhumans based on narratives of sexism or other, similar ideas, simply because you are sidelining your best weapons out of ideology (and would likely lose). If you have a woman who's a flying brick and a man who's power is to heal people, why would the culture tell the woman to get back in the kitchen and send the man to the front lines?
This wouldn't just apply to women. Cultural narratives of LGBT people or those of a specific ethnic group being "inferior" would be rapidly debunked by the presence of high-profile individuals with superpowers that anyone could point to. Patriarchy, homophobia, or ethnic superiority probably wouldn't become a thing, because it would contradict historical knowledge. Powers versus no powers would be the primary social divide.
A good example of this can be seen in the Avatar: The Last Airbender series. The Northern Water Tribe and Earth Kingdom have been depicted as highly sexist, and the Turf Wars miniseries revealed that the Water Tribe, Earth Kingdom, and Great War-era Fire Nation were all incredibly homophobic. This makes no sense given that for 230 years Avatar Kyoshi, the physically and politically most powerful person in the world (and often revered in-universe in a manner similar to the IRL Dalai Lama), was an openly bisexual woman who eventually ended up in a homosexual relationship. And then that person's reincarnation three cycles down the line (Korra), was also a bisexual woman who ended up in a homosexual relationship. Not to mention all the powerful benders who are either female or LGBT. The most powerful Earthbender is the world in both series is a short, blind woman. Homophobia and sexism make no sense within the context of that world.
How to fix this?
There are a couple of solutions to fix this, but none of them are any good. The easiest way would be for there to be some kind of masquerade hiding the existence of superpowers and the supernatural from the common populace, at least until the author decides to reveal it. But a masquerade is way more trouble to maintain than it is worth, maintaining a would be nearly impossible and there are tons of examples on this very website on how hard it would be to maintain. Just to pick out two examples, a masquerade would require large numbers of people to successfully keep a hugely noticeable secret and for no one to be in a position that's can easily break it (laughable at the best of times) and if the government is using funding to hide evidence of the supernatural someone will notice the money going missing and will eventually dig up evidence on it. Not to mention a masquerade would require the complete cooperation of every nation on the planet (laughs in realpolitik), and there is nothing stopping, say, China from deciding to cause social chaos in the U.S. by revealing the existence of the supernatural (or vice versa).
The masquerade also has issues with having to do mental gymnastics through history in order to justify why superpowers haven't affected history beyond a few mysterious events which are basically low-hanging fruit for urban fantasy/science fiction settings like Tunguska or the Bermuda Triangle. Why didn't the presence of superhumans affect World War II? This was a problem in IRL comics where DC had to justify why Superman didn't just punch out Hitler given it was in character for his altrusitic, pro-freedom personality and came up with the solution that Hitler had the freaking Lance of Longinus. Or, to use American history as an example, where were the superhumans during the Civil Rights movement or the recent Black Lives Matter protests? Are you seriously telling me that not a single superhuman in the U.S. felt the desire to affect positive social change given their position of power, or that you had some young, politically left-leaning, disaffected 20-something superhuman who hates the system and cannot easily be stopped by the police decide to go on a rampage during the riots in 2020 (or any riot in history, really)? Which would in turn provoke further outrage and controversy or escalate the situation. Even if their powers were "only" Spider-Man level, their actions would still change history significantly.
The other option is to tie superpowers into historical folklore about people with superhuman abilities. Urban fantasy already does this to some degree using a "stock catalog" of folkloric supernaturals like vampires and werewolves, and you could also potentially do that with historical narratives of saints, demigods, and other superhuman heroes. In this case you at least have an excuse for why people haven't made mention of the supernatural: "oh, they have, but it's just memorialized in folklore rather than being seen as real and common knowledge". But the problem here is that you are restricted in what you can do based on IRL folklore.
Now, I know your question is: how powerful can a superhuman be without making a world that does not resemble our own history. Well the answer is: not very powerful at all. These kinds of things would come about even if you only had a small number of superhumans with rather unremarkable powers. At most you could have someone like Daredevil, who's powers are a bit odd but ultimately he's physically no different from a fit parkour-loving human. Even a small number of people who are "peak human" (as defined by Marvel), like Captain America, would massively distort history from what we know. The only way for this not to be the case is for superpowers to be so rare and so minor that you may as well not even call them superpowers in the first place.
