Chances are they will work without issue.

USB drivers aren’t something you’ll need to go searching for, most chipset drivers are something built into the kernel.

Bazzites’ use of a modern up to date kernel and the fact that USB HID works better on Linux than windows should benefit you. Furthermore it builds on Valves work supporting as many input devices as humanly possible with Steam.

The only concern you should have are things like RGB or non-standard hardware that requires extra software to operate. One of these things is an XBox One controller as it’s not a standard USB HID

https://github.com/ublue-os/bazzite/issues/1418

Bazzite is a great choice, I used it for 2 years as a htpc and it was perfect for what I needed.

Never used a wireless xbox controller, but it paired immediately with two PS4 controllers. I also had a generic wireless keyboard with its own usb receiver, and that was fine just plug and play.

I'm using Bazzite with the Microsoft Wireless Controller and it's working fine with one caveat. The controller requires a firmware update that requires a Windows OS or an Xbox.

Gaming on Bazzite has been great although trying to figure out how to install software on it is a little bit more difficult since it's an immutable distro.

I’ve used a wireless mouse, keyboard and xbox series controller with my Bazzite desktop. I usually use the proprietary Microsoft adapter with my controller and it just works. Occasionally I will have to disconnect and reconnect the adapter so it will pair, but that’s about it. Using bluetooth for the controller works too

I have Bazzite on my home entertainment handheld. I use it on the big screen with my TV using a dock and I have the logi bolt setup with a keyboard and mouse and it works flawlessly. But the logi app doesn't work with Bazzite as far as I'm aware.

All the controllers I have work without issue, so long as you have handheld daemon setup. So that's pretty easy.