I don’t have a Linux PC, but I have Skyrim heavily modded on my Steam Deck. It has been quite a while since I set it up and I know very little about Linux, but if you search for tutorials for Steam Deck instead of Linux, you might find what you need.
I’m definitely using SKSE and this may or may not be the guide I used to add it: retroresolve.com/…/install-skse-on-steam-deck/ (I don’t remember the details, but I spent several evenings getting all my mods set up when I first got my deck).