8BitDo controllers have a few different controller API modes, but they're limited by those APIs. By default they recommend using XInput with PC, but XInput is based on 360 and limited to the set of buttons a first-party 360 controller normally has. This means that the Star/Share button doesn't exist, nor do the additional rear buttons. Instead, they can be mapped to certain functions within the controller firmware. Unfortunately you have to use the 8BitDo Ultimate Software to configure them, and that isn't supported on Linux (doesn't work in Wine either, I tried). There's also an Android version of the Ultimate Software you can try, but I think it only supports some older 8BitDos. There may be some default Star+button combos already, I forget what they do.

If you set it to Switch mode, that enables the Share button to work the way it does on a Switch controller, but software might not recognize it. And the rear buttons still don't exist as distinct buttons since Switch controllers don't have those, they are only ever for macro remapping within the firmware. I don't think there's any way to make them distinct.