Ive only ever used Vortex and it works great for me, even on the steam deck.

I used ProtonUpQT (its on the flatpak store) to install SteamTinkerLaunch.

For the game you want to run, you set the compatibility tool to SteamTinkerLaunch (same menu you would use to select the proton version).

Then in your steam library you create a category called Vortex and add whatever games you want running vortex to it.

Then when you launch the game you get a SteamTinkerLaunch menu where you can change loads of settings and access Vortex Mod Manager.

Ive played Fallout 4 (should be similar situation to Skyrim) like this since the Steam Deck came out and the only issue i came across is when i had a game on the SD card Vortex couldnt find the game location so i had to create some symlinks.

This method also worked for me when playing Starfield.

You can install mods by copying the Nexus mods link into Vortex and they also auto update.