Also, you'll start Skyrim through Steam as usual, not through Vortex. Note that with this guide you'll get an older version of Vortex (1.1.15), but IMHO it is still a better choice than Mod Manager 2.
You should be able to apply the same walkthrough to Oldrim or Fallout 4 as well.
The below walkthrough is for those who are running Skyrim SE via Steam Proton, and want to be able to manage mods via Vortex Mod Manager in Linux. Manage Skyrim SE mods via Vortex Mod Manager in Linux