"Nothing" may be a little too strong -- physics is physics, after all -- but (small) birds and airplanes have Reynolds numbers about 1000x different and different underlying material science.
Airplanes are engineered (with a very small number of exceptions) to be stable during flight, whereas bird flight is inherently unstable, requiring a lot of specialized cognition so birds can fly.
I would think a lot of cognitive ornithologists (who I really hope exist!) would be interested in finding out about this.
At this point, I'm at the complete end of my knowledge of bird flight!
This is completely missing the forest for the trees. The "except" in your argument is doing an incredible amount of work. I think it's absurd to claim that the rotating blades of a turboprop are analagous to a bird's wings when planes l have separate structures quite literally called "wings" because they are directly inspired by bird wings. And I think the absurdity of that argument actually serves to prove my point.
That is not true.
Turboprop engines and flying birds are different things, but there is a set of common properties.
A blade of a screw propeller functions exactly in the same way as a flapping wing of a bird, except that the wing cannot rotate without limits around the body of the bird, so it must stop, change angles and revert the motion, while the blade can rotate continuously around the axis, functioning on one side like a falling wing and on the other side like a raising wing.