iPadPro battery completely draining overnight iff Bluetooth is turned on

I have a 2020 11" iPadPro and the battery will drain completely - from 100% to 1% - while idle overnight, if and only if, Bluetooth is turned on. Turn off Bluetooth and there are no problems. Turn off Bluetooth and leave Wifi going? No issues. Turn off Wifi and leave Bluetooth on, dead in 12 hours.

Unfortunately, Apple has decided that "Airplane mode" means "Leave Bluetooth running for... reasons" and you have to manually turn off Bluetooth in Settings for it to turn off. (Which makes me wonder what the FAA and FCC have to say about Airplane mode not disabling all the radios.) Also, Apple, "helpfully" resets that every update so unless I manually turn off Bluetooth after it runs, I wake up to a dead battery.

I took it to BestBuy for a battery replacement, they hook it up to their machine and say nothing's wrong with the battery.

None of my other Apple devices seem to have a similar problem. My iPhone 13 Mini can sit idle, not charging, and still have 60% after 24 hours. My MacBook doesn't seem to have any problems on the rare occasion it's unplugged. None of my non-Apple systems seem to have any sort of problem, either.

The only thing I can say is that it started after I moved, and I'm wondering if a neighbor with an AirTag might be causing this. (Which is a known issue with extensive documentation that Apple refuses to acknowledge.)