I am also having this problem on Ubuntu 24.04.1 LTS with the PowerA wired Nano controller. The button mappings seem to be completely off. The controller itself is working though, or at least it seems that all the buttons do something.
Nothing extracted yet.
On both SteamOS and a Linux desktop (Pop OS in my case) aftermarket USB Nintendo Switch Pro Controllers no longer work. On SteamOS 3.5 and older (and whatever desktop version corresponds to that time) these controllers worked. I've tested a Retrofighters BattlerGC and a PowerA Wired Controller for Nintendo Switch. Again, these controllers do work on Windows with steam input, just not on Linux recently. Getting a steam deck downgraded to 3.5 is the only way to have them functional currently.