Can’t speak to Xbox Series controllers, but Xbox One controllers on Linux are a mess in terms of the drivers situation. Running 'em over USB with xpad, the default kernel driver is fine, but you might need to install xone or xow to get them working wirelessly with the dongle, or xpadneo for Bluetooth. Maybe other people have had a better time but it’s a total fucking headache IME.
Did you know?
Phones can have a headphone jack and still have Bluetooth for the people who don’t want to use it!