Got the Ultimate 2 Wireless (both the Switch and the XBox version), connecting through Bluetooth.
I just connected it and it worked right out of the box, however every now and again it will "hang" and the joysticks stop working. The only thing that helps is switching it to 2.4 GHz mode, wait a couple of seconds, switch back to BT and wait for it to reconnect.
Steam finds it just fine, installed through Pacman.
I'm on Garuda Linux (Arch-based).