So I’m sure you’re aware that there are two groups of birds that are incredibly intelligent;
Corvids and parrots.
The marks of sapience in these animals include simple tool use, language and dexterity. I’ll summarise them a bit here.
I’m not familiar with parrot language, and they are often more famous for their mimicry, but many species of corvids, especially crows, have been observed to have simple languages that have specific words. One species of crow only has a little over 20 words, but within that vocabulary is different calls for food, danger, etc as well as a basic counting system (consisting of ‘one’, ‘none’, ‘many’, and ‘less’ or ‘more’) and they have been observed mourning the dead. This is rudimentary, but both parrots and corvids have demonstrated complex vocal abilities when mimicking so the physical ability is there, along with an established foundation for language.
Both Corvids and Parrots have demonstrated forms of tool use and generational learning/ problem solving skills. Crows and ravens have been observed fashioning hooks from twigs to reach trapped food, and using pedestrian crossings to crack nuts (via car tire). Corvids show impressive dexterity with both their beaks and talons, though parrots are much further adapted with their feet plans and therefore are more dexterous (often scratch themselves with sticks). Again, as with language, the foundation is there and so is an innate physical ability, the only missing piece is higher cognition.
What They’d Look Like
In my honest opinions, other than a possibly growth in cranium capacity and a more generalised beak shape, the body plan doesn’t need to change. A bird can stand on one foot, even stabilise itself with its wings, and use both their beak and other foot to manipulate objects perfectly well - keeping their flight ability intact.
The wing is an incredibly regressed limb. The remains of their phalanges are just one fused finger. I find it incredibly unlikely they would develop a new grasping apparatus when they already possess three (feet and beak).
For corvids, the main problem is their life span and life expectancy. Crows learn slowly in the wild, and in most cases it’s is a multigenerational process.
I mentioned the nuts on roads, but a simpler learned behaviour is cane toads. Cane toads are a prevalent pest in north-east Queensland, and have been for a number of decades. They possess venom sacs on their necks that protect them from predators, but recently crows and magpies (also corvids, different to US or UK magpies) have been observed flipping the toads over, exposing their less venomous underbelly. This is impressive, but it took several decades for the population of corvids to learn.
Parrots live to ages very similar to humans, so they may very well be a better candidate for future sapience, but while studies have found some species able to learn (not mimic in this case) up to 100 words, little is known of their wild language - which in evolutionary terms is the one that counts.
For corvids, a longer life span is likely needed, but for both groups a pressure is needed. This obviously hold true for any evolutionary change, but birds need to have their current niche challenged, or a new one opened up, before they’ll begin to speciate.
Keep in mind that birds are not mammals, and they are most certainly not primates. They have exhibited ape-like levels of intelligence, but not intelligence that is ape-like. It is incredibly unlikely birds would evolve sapience under the same drives and conditions as humans did, especially due to their airborne nature. Consider this if you choose to implement this into your world - sapient birds will not be bird-men. I will however provide examples I believe are plausible for birds.
There are factors that influenced human development, that are not exclusive to evolutionary drive or result. An example is the discovery of fire, which was a result of higher cognitive ability but also enabled the cooking of meat, allowing more energy from animal-based food, and therefore drove further cognitive development in a sort of feedback-loop. There are numerous examples like this - I’ll give a more obscure example.
Neoteny is the retention of juvenile traits after maturing to adulthood, an example being axolotls. It is theorised that humans selected for neoteny in the form of hairlessness and enlarged heads because they found these individuals ‘cute’ and were more likely to mate with individuals that possessed them. This increase in head-body ratio complimented the development of a larger cognitive ability. Due to the incredibly prevalent reproduction-driven evolution in birds, this isn’t a far-fetched drive for bird sapience development (not including the hair thing probably).
For corvids, they are already opportunistic and relatively omnivorous, so the discovery of fire is one of the few human milestones that is believably possible for them. For parrots, they would likely need a pressure that forced them to branch out in diet, as they are largely seed/nut based. Meat is not the only answer, but a higher and more reliable energy intake is needed to fuel an expensive organ like a brain, and cooked meat is a very convenient solution.
Just found some studies of raptor birds (kites and hawks) in australia picking up bundles of twigs and lighting them from existing fires to start new ones in other areas, most likely to herd small mammals out of grass and such. they're already manipulating fire!