I use a PS5 controller connected through an 8bitdo USB adapter 2. It works great and has a much more stable connection compared to the bluetooth adapter I used to use. I’ve had no issues using it in xinput mode on Linux; games pick it up as a normal xbox controller and just work. The adapter also works great for bringing your own contoller to friends’ houses for any console party games without having to do the bluetooth pairing roundup minigame. The only real issues I have with it is that there’s no auto disconnect when it’s idle, and as you mentioned the firmware flashing tools are all Windows only.
I’m on a 4770k and GTX 980 as well but I’m really feeling the pain because all the newer games I want to play are CPU bottlenecked.