The bird that can fly very high in the sky is the Ruppell's Griffon Vulture which is the highest flying bird ever recorded.
The Ruppell's Griffon Vulture bird was recorded flying at a height of 37000 feet which is a bit higher than most airplanes fly.
Airplanes typically fly at a height of 35000 feet.
Some types of birds can and do fly over Mount Everest.
Not all birds are capable of flying over Mount Everest because it's too high of an altitude but some mountain climbers and moutaineers have reported seeing some birds flying over Mount Everest.
The birds that can fly over Mount Everest are birds such as the bar-headed goose.
My friend saw a bar headed goose fly over Mount Everest a few years ago when he visited Mount Everest.
It's rare to see birds fly over Mount Everest but it does happen.
Most birds though fly below the altitude of Mount Everest so it's a rare sight to see birds flying over Mount Everest although you might see some birds flying near or around Mount Everest though.