Whilst I am also doubtful we’ll get much more in the way of birds (a few more at best), for me the reason this is so annoying is precisely that no new mechanics are needed.
First, and most obviously, waking birds like cranes and flamingos have always been in-game as have mostly ground dwelling birds like peafowl. Those groups alone would provide ample options for multiple dedicated bird animal packs. Add to those aquatic birds like the swan and there are literally dozens of great options.
Second, walk though exhibits (and even standard exhibits) would work perfectly well for dozens more species of flying birds like finches, hummingbirds, and many, many more.
Third, even free-navigating flying habitat birds wouldn’t require anything new - all deep diving species in-game can navigate in 3d and habitats can already be built with ceilings to prevent escapes (though, perhaps an aviary cage set of build pieces might make this easier for many people.
There is no need at all for new mechanics - plenty of bird species (numbering, literally in the hundreds) could be added using only the mechanics we already have in-game… they just haven’t been.