I use a ps5 controller for all my gaming needs and it works great on Linux (Kubuntu/Nobara) and Steam Deck. I use hardwired when playing on my Linux desktop, but when playing on my Steam Deck it’s over Bluetooth while docked. Still works perfectly fine. I even played Crosscode with my controller just fine on both systems.
I primarily use it on my desktop for FFXIV which is why I do hardwired. Bluetooth can be squirrely if the game isn’t launched through Steam