Sorry for my late reply.
As far as the 8Bitdo adapter is concerned, it mainly works on a Switch but can be used on a PC/MAC. As far as controllers that can be used with the adapter, PS4, XboxOne and 8Bitdo controllers work and connect without any problems. The PS3 controllers do not work as far as I know.
Reminder: don't forget to update the firmwire of the adapter via the small program available on the official 8Bitdo website.

According to the manufacturer, this adapter is not compatible with the Razer Raiju controller. The raiju controller is a manufacturer specific controller (although it is designed for the PS4). It often does not work with converters for other consoles.