Would this controller not be compatible via Bluetooth?
Probably... There are thousands of hardware and drivers and the team can't test them all, if it's incompatible, there's not much you can do besides file an issue:
https://gitlab.com/recalbox/recalbox/-/issues
But, before opening an issue, try doing a factory reset (available through advanced settings), you will not lose any personal files, but you will lose all custom settings.
See if this helps:
https://recalbox.gitbook.io/documentation/tutorials/controllers/configuring-custom-buttons/how-to-customize-controller-mapping https://recalbox.gitbook.io/documentation/tutorials/controllers/configuring-custom-buttons/create-a-custom-configuration-by-emulator https://recalbox.gitbook.io/documentation/advanced-user/configuration/configuration-overload https://recalbox.gitbook.io/documentation/advanced-user/configuration/configuration-overload/retroarch-overloads https://forum.recalbox.com/topic/24237/ps3-controller-muting-kodi/16
