You might find the steam tinker launch useful. One thing it can do is download and launch Nexus' Vortex Mod Manager inside each games proton prefix. Which should let you manage mods for various games especially elder scrolls and fallout games. Not tried it with fallout 76 though.

I haven't done much for modding, but I did mod up Beat Saber recently with ModAssistant. What I did was add the ModAssistant exe file as a non-Steam game, then put this in the launch options:

STEAM_COMPAT_DATA_PATH="/home/[username]/.local/share/Steam/steamapps/compatdata/620980" %command%

The 620980 is the AppID for Beat Saber; you'd have to find it for each game. What this does it run the exe file in the same prefix as the game, which is good for making sure that any changes to ini files (etc) in AppData actually get written to the right spot. It worked great, no different than on Windows.

I modded Fallout 4 on SteamDeck by running Vortex in Desktop mode using Steam Tinker Launch. I recall it being a little finicky to find all the right paths etc. Some googling should lead you to a guide for running Vortex on SteamDeck.

Only ever modded skyrim on linux so far with mod organizer. I did mod the sims 3 and 4 and it worked relatively the same as windows.

I run Stalker: Gamma on a Steam Deck.

Tips: Install it using Windows and just move the Anomaly and Gamma folders over to the same directory. Make sure to pick a wine version with esync and fsync patches or it will run like shit.

As for controlling Stalker with a controller... I'm working on it, myself. I pretty much bound everything as you'd expect in a normal FPS and made the back buttons work for healing items and melee. Select for the PDA, Start for pause.

I've previously modded a game on a PC and just copied the files over to the steam deck and it worked fine.

It wasn't a Bethesda title, though. Don't know how mods work for those.