Good concept, it's funny and frentic.
Maybe there is to manybirds , it's help the chaos vibe.
A sugestion, add a pill queue,bubble bobble puzzle, at first each pill has a single color, but as the level progress add more color to a single pill, that determine the color the bird gonna shift. from there you can play around it for examply Pliss form define the behaviou of the bird after consume, If you don't use the pill fast it automaticall change or can trow itlsef catching you with the guard down.
My point it's the chaos and frenzy fit perfect to the concept, but you need an aditional layer to make the player fell challenge and not simply smash buttons, like a fighting at start you smashing buttons because that work but as you progres you have to learn the moves of the fighter you choose.