The Saturn BT adapters I looked at are retroblue, pretty much the Saturn version of the playstation adapter afaik.
You can use like XB1/PS4/PS5 controllers with them. Probably some others too idk.
The retro-bit wireless controllers can be shit (broken buttons and/or d-pads) and I don't think I'd take a chance on them being ok. Apparently their wired controllers are better.