Depends on your criteria of immutable, but as far as I know you could use both on NixOS.

Have you considered something like jupyterhub?

I went down this path, but mini itx nucs with a GPU slot seemed to be better as long as you’re not using the egpu on multiple devices; if you are, then it might be worth considering just making a PC a host and running sunshine/moonlight. While I haven’t tried connecting to my host on the steamdeck, I have on my laptop and felt like it could be used for gaming

I have it fully operational on my actual server machine running Ubuntu,

Was this difficult? Sorry to hijack, but I hadn’t really considered doing this but now I’m intrigued lol

I have a similar use case on my laptop and love NixOS with hyprland