

Batocera has a good list
https://wiki.batocera.org/supported_controllers
Otherwise, I would consider that Linux is not the limit/cause of incompatibility and most will work out of the box just fine.
https://www.eurogamer.net/digitalfoundry-best-pc-gaming-controller-gamepad
This might help
https://blog.pishop.co.za/using-a-raspberry-pi-as-a-bluetooth-speaker-with-pipewire/