IPad Air 4 (2020) power/sleep button broken and jammed, forcing recovery mode on every restart - any help appreciated!

I have an iPad Air 4 (2020) and the power/sleep button on the top is stuck in the down position. Now anytime I plug in the iPad, update it, restore it, etc., it boots into recovery mode (presumably because the power button is perpetually depressed).

I have not found anything in an extensive search online that addresses this situation, so any help (or even suggestions on things to try) would be appreciated. I took it to uBreakiFix and they said they don't do that kind of repair. I hate to scrap it because it's just over a year old and there's no other damage to it whatsoever, just the power button being stuck which I could live with, I just need it not to be causing the iPad to constantly boot into recovery mode.

I assume Apple will tell me I have to pay the $400-500 repair fee, and at that point it's likely worth it to just get a new one, so I'm trying to see if there's anything I can do.