Humans colonized all the stars in the Milky Way in the first million years. In the next 200 million years they conquered all the planets in the Local Group. In the next few billion they conquered all the Virgo Supercluster.
At this point the accelerating expansion of the universe pushes further galaxies out of reach. This prevents humanity expanding further.
After billions of years, evolution has produced as many human species as there are planets conquered, some of them completely unrecognizable from the humans of today, while others had retained more or less the same appearance, like living fossils.
However, everything great will come to an end. In this fictional universe, roughly 91.8 billion years into the future, the increasing expansion of space will cause individual galaxies to be ripped apart.
175 million years before the end, ordinary galaxies are starting to have stars fly off into the void. The universe is expanding so quickly that it becomes impossible to ever get more than 200 million light-years from your starting point, without exceeding light speed.
Over the next few million years, astronomers everywhere will observe stars at the fringes of their own galaxy receding away at over a hundred km/s in every direction, and they'll also see most other galaxies starting to lose shape and get torn apart.
175 million years is a long time, and most future humans living in this time will probably go on their daily lives as the doomsday won't happen until they were long gone and their culture forgotten or evolved into something else. From their home planets, an average naked eye observer wouldn't notice anything wrong with the night sky other than their own galaxy completely disintegrating over the next 100 million years, but that's several orders of magnitude longer than an average human lifetime and therefore too slow to be noticeable. The first sign something is horribly wrong would be visible to the naked eye maybe a million years before the end: there are way fewer stars in the night sky than before, and many of them look way redder than expected. This is due to redshift, and this effect will be amplified the faster the object is receding away. 20,000 years before doomsday, most stars would've been redshifted out of the visible spectrum, leaving only a handful of neighboring stars twinkling creepy blood-red in the night sky, receding away faster than ever before.
Star after star in the night sky will redshift out of view and soon after get gobbled up by the Cosmic Event Horizon inching closer and closer. Less than a thousand years before the universe rips itself apart, the next closest star meets the same fate, leaving the night sky on any planet pitch black, except for other planets in the same solar system.
Even this won't last long. Starting a few decades before doomsday, planets will begin spiraling outwards from their respective orbits. At first, it starts slowly, barely noticeable, but as the Hubble parameter speeds up even more, the planets start gaining noticeable distance from their stars, and the climate on those planets starts cooling down, before reaching escape velocity around 9 months before the Rip, completely detaching itself from its star forever. Over the next month, what was once the host star will get dimmer and redder until it too fades from view. For the next 7 - 8 months, there will be nothing but complete darkness, except for maybe artificial lights on inhabited planets. Everything freezes over and gets snowed down, no one goes outside anymore as it's constant darkness and temperatures rapidly plunging down to below -100 degrees globally.
We've finally arrived on the day it happens. It's just like any other day for the past 8 months, except, if there are space stations in low orbit, they will start spiraling outwards today, and there's nothing one can do about it. A few hours later, they would've been yeeted into the void never to be seen again. Soon afterwards, the planet's atmosphere will start thinning, faster and faster. The planet might begin heating up slowly as the rapidly accelerating expansion are exerting forces on the planet's structure. People will also slowly start feeling lighter, then rapidly lighter, then eventually, about 30 minutes before the Big Rip, everything not directly attached to the planet will be lifted up from the ground and gradually start accelerating upwards like some dramatic Wingardium Leviosa spell straight out of a Harry Potter movie. This will be where human history ends as no one can possibly survive being yeeted into outer space in this manner. Over the next 10 minutes, the planet will start heating up to thousands of degrees and molten rock will be dripping off away from it, gradually tearing the planet apart, but as the Hubble parameter accelerates faster and faster, it'll start tearing larger and larger chunks from the planet before it eventually explodes into billions of tiny fragments.
Existence is futile at this point. Everyday objects held together by electromagnetic forces will get torn apart a few seconds before the universe ends, even subatomic particles will get torn apart too, only mere fractions of a second before the fabric of spacetime pops.
The big question is, are there any way for humanity to escape or hide from this event? Humanity has become extremely advanced and has had over 91 billion years to figure out a solution to survive this moment of doom. What could that solution be? Hiding inside black holes? Will black holes get torn apart too? What could they do afterwards if they somehow finds a solution to survive? If black holes are one of the solutions, then I would imagine an entire galaxy's population mass migrate to the central supermassive black hole of their galaxy a few million years before doomsday so they could ensure they won't get causally disconnected from it when they need it. I would imagine that for the last million years, a whole galaxy's worth of people will be concentrated within a light-year from the black hole, spawning racial conflicts between different human species of absolutely epic proportions.
On the contrary, what if there's no solution? I would imagine they need to shut everything down a generation before doomsday. Maybe they would enact policies that prohibits all people from reproducing so the last person dies a few years before the event happens.