instead of sunshine, try apollo.
https://github.com/ClassicOldSong/Apollo
it's a branch of sunshine but supports virtual displays (and some other stuff).
i can launch moonlight on any of my clients (phone - 2316x1080, laptop - 2880x1800, laptop connected monitor - 2560x1440p) and the virtual monitor will spawn and match the client resolution automatically.
when I disconnect, the resolution will revert back to the desktop connected monitor.
this won't let you use your desktop while streaming games elsewhere though. You'll need to do VM's or Docker+wolf for something like that.