The problem with Xbox style is, that Xbox does not support wireless. For the 8bitdo ultimate 2 that means you have different modes of the controller. In xbox mode (default) it acts like a xbox controller. No support for gyro. You have to hold specific buttons when starting it, so it starts as Switch controller. In the Switch mode it supports gyro, but A and B are swapped and it does no longer act like a Xbox controller, which some games might handle it differently. Another little annoyance is, that the firmware cannot be updated in Linux itself.

As for the repairing, I don't actually know if you need to when using on a different OS. I know the controller has builtin memory to save and use the configuration regardless of the OS. Meaning setting it up in Windows, and then using in Linux without additional software. Now when I think about it, I do not need to re-pair it, when I update the firmware in a virtual machine. Switching it back from Windows to Linux, there is no need to re-pair it. But I don't have other experience.

I'm just sharing my frustration with this gamepad. Gyro was one of the reasons why I purchased it, and I cannot use it because i don't want to use it in Switch mode. At least the dock is pretty cool and it acts as its own connection. It also supports Bluetooth, but I don't use Bluetooth. I think the upcoming Steam Controller from Valve will be the ultimate controller, with gyro and trackpads builtin. No driver or firmware shenanigans, no mode switching.