Have you seen the 8Bitdo Micro?

It can connect as a bluetooth keyboard and the software lets you remap most keys I believe. On some LTT videos, you can see Linus with an 8bitdo zero2 that he’s obviously using for some sort of teleprompter control. Up to you on your size, and I don’t think the Zero 2 supports remapping.

Mostly using is about the same. Unless you have an Xbox One controller that came out before the S; those don’t have Bluetooth. Also newer controllers and firmwares switch to Bluetooth LE, which is not the same as Bluetooth, so make sure you have that.

Or if you want to use the headset jack, that won’t work over Bluetooth. Bluetooth audio sucks.

Or if you want to hook up 8 players, Bluetooth is limited to 7 devices.

Rting.com is pretty good: https://www.rtings.com/tv/reviews/best/ps5