Have some experience with Xbox controllers and steam controller
First official Xbox One X controller is absolute shit via bluetooth. Proprietary dongle works well, as long as its on windows - getting it to work under linux is a pain.
As far as compatibility goes Xbox 360 Dualshock with 2,4ghz wireless dongle is the best - dongle identifies as wired controller, it works correctly with everything.
Steam controller works with everything except ergonomics is IMO garbage. Dualshock rules in this area
And don't even think about connecting anything via bluetooth to android - bluetooth drivers are broken since android 10, causing massive input lag. Use either wired, or Xbox 360 2,4ghz wireless dongle controller