For Linux, I recommend the DualShock 4 (PS4) and DualSense (PS5) controllers. They have native support built into the kernel, so you don’t need special drivers. They’re great in Steam, emulators, Wine, and most native linux games. They work in both USB and bluetooth mode. Motion controls work. Touchpad works. Rubmle works. Dead zones are nice and small.
The only features I’m not sure about are the DualSense haptics and adaptive trigger feedback. There was work happening on those when I last looked a couple years ago; I haven’t checked recently.
A few people have reported lag with certain bluetooth adapters. I haven’t seen it with any of the hardware I’ve used, but if you encounter it, you can always get a different bluetooth adapter or exchange the controller for some other model.