Ah a very fun 'snippy' question that just proves my point further. Thank you.
No airplanes do not sleep. That's part of why their flying is fundamentally different than birds'.
You'll likely also notice that birds flap their wings while planes use jet engines and fixed wings.
My entire point is that it is foolish to imagine airplanes as mechanical birds, since they are in fact completely different and require their own mental models to understand.
This is analogous to LLMs. They do something completely different than what our brains do and require their own mental models in order to understand them completely.
Here, it's actually fun to respond to your comment in another way, so let's try this out:
Yes, sleep is in fact a prerequisite to planes flying. We have very strict laws about it actually. Most planes are only able to fly because a human (who does sleep) is piloting it.
The drones and other vehicles that can fly without pilots were still programmed by a person (who also needed sleep) FWIW.