Flying in a plane recently I realised I’d never seen a bird outside the plane window.
I assumed it was because birds didn’t fly that high.
Turns out I was wrong. There are birds that fly at the altitude of commercial aircraft.
For one, the Rüppell’s griffon vulture which has been seen at 37,000 feet.
Even the common crane flies to 33,000 feet which it does when flying over the Himalayas to avoid eagles in the passes when migrating.
More info https://en.m.wikipedia.org/wiki/List_of_birds_by_flight_heights
So the reason you don’t seem them at this height is because they only do it where necessary. Or rarely. Eg there are very few Rüppell’s vultures remaining.