Well it’s kind of hard to use an input device when you don’t have a driver for it…
Steam provides their own evdev-based driver for the Switch Pro Controller, but you’re going to have a bad time trying to use it outside of Steam.
There’s a kernel driver called hid-nintendo, it was originally planned to be merged for 5.10, but the developer cancelled the plans and is going to merge it at a later date, I guess. There’s a repo for the dkms module at https://github.com/nicman23/dkms-hid-nintendo
Clone the repo, and follow the three-line instructions.
Then, whenever you want to use the controller, run
sudo modprobe hid_nintendo, then connect the controller (you can use bluetooth or usb, both work fine). Make sure Steam isn’t open, or they’ll conflict.
If you want to use Steam and the
hid_nintendo module is loaded, just unload it with
sudo modprobe -r hid_nintendo.
You can find more information here: https://wiki.archlinux.org/index.php/Gamepad#Nintendo_Switch_Pro_Controller_and_Joy-Cons