Once it's installed, you'll probably need to close steam for it to pop up, You'll want to enable Enable Steam Play for supported titles and Enable Steam Play for all other titles and select GE-Proton for that you want to run the games with
I've installed Sunshine on my home destkop. I had to rebase from Aurora to Bazzite, and I had to play around with the Moonlight settings a bit, but it is running quite nicely now. Even over a VPN it is quite nice.
Looks like it's working, firs time I launched the game it gave me an error stating the updater encountered an issue, and now the launcher is downloading the game correctly