Almost any distro will work for pretty much all of that. Only potentially limiting thing I see there I don’t think that the Mullvad VPN client is generally available within distro repositories. Their site says it has clients available for Ubuntu, Debian, and Fedora. So perhaps pick from one of those?
For the steam link question, I know if I have a game running on my desktop it presents me the option to stream to my laptop (both Linux machines). I assume this is the same functionality. I don’t use it so can’t speak to how well it works.
Edit: It occurs to me this comment lacks a recommendation. Within the three listed supported distros for Mullvad, I think I’d recommend Fedora for you. Been some years since I used it last but I remember the installer being fairly robust and intuitive while still easy to use, and a pretty rock solid system once it’s up and running.
LFS + twm FTW.
You seem to have a good sense of what disros are out there. I think any beginner friendly distro with wherever user friendly DE it comes with will probably be fine.
I’d say maybe stick with a deb or rpm one which most are anyway, for the compatibility point you already made. If you/they need something that’s otherwise not available in your distro’s repos, there’s probably already packages or third party repos available.
But the ask is a recommendation. I find myself generally recommending Fedora, despite not having used it myself for years. It’s easy to install, you can choose your DE, it’s stable, has a good release cadence, and is easy to upgrade and maintain.