There's still room for improvement, but Linux gaming has come a long way in a short time.
I remember when Proton launched it was like magic playing games like Doom and Nier Automata straight from the Linux Steam client with excellent performance. I do not miss the days of having the Windows version of Steam installed separately.
Same as far as I can tell. I installed model swap mods for several games, workshop mods for binding of isaac and terraria, and did other random things to games like tweak configs and shit. All of it worked fine. The biggest issues I had is installing random old games in my collection to my steam deck that weren't on steam already, and even that I still managed to make it work.
For most games I'm sure you can find a way to do it. If you use protontricks you are able to run an exe under a proton prefix for a game (basically a virtual windows drive in a folder for the game) which I've had pretty decent luck with.
If you play games that support mod organizer 2, there is a sh install script somewhere for support in proton/steam that works well (I can find if you like), but the program does run pretty slow and is fairly buggy. Usable with patience. Upside is it can run MO2 for a given game direct from steam if configured correctly
My son does tmodloader via steam, but I think its native Linux. Works without issue.
I play WoW and run Trade Skill Master (in the same wine bottle prefix). I also run RaiderIO/WoW Up/CurseForge (Linux native).
I had issues with mods for The Forest and Sons of the Forest. Never got them working.
FF XIV DPS meter worked after a lot of tinkering. Had to go to a specific discord to get the info as the modders didn't keep their READMEs in GitHub up to date. Wish that shit was searchable.
For terraria tmodloader works no issue, I think forge has a native client for WoW, and Minecraft is linux native anyway
EDIT: I only ever modded terraria and minecraft so idk about any more
It varies but generally if there is a will there is a way. Sometimes it just works, sometimes intervention required.
Typical things that may or may not be needed depending on game:
Windows packages and/or Dll overrides via launch arguments or winecfg/protontrick
Separate wine prefix with specific weird wine build to run mod managers or editors etc. with links to relevant directories in game prefix
Case insensitivity which can be set per directory on empty directories on ext4 (poorly made mods only usually)
Searching "[game name] mods [steam deck or linux]"
Regretting all of that to find that there is a Linux mod loader that works 100% but google stopped giving meaningful search results decades ago and the reddit trick doesn't work as well post api-suicide.