I can’t speak for skyrim, but I have done this with Cyberpunk 2077. I switched from windows to Nobara linux and I could continue playing the same save game on linux. But it needed some work: I had locked the windows version of cyberpunk to a specific version (I think 2.7) and on Linux I used the Heroic Launcher to install the very same version on linux (2.7). Then I moved over all of my mods, and my save game, and to my big surprise it actually worked. D: