Fortunately I've already played through Alyx a few years back (and it really is an amazing experience). These are issues I'm having since moving my rig away from Windows a few months ago. Even then, games are still playable on this setup, but the points above add a lot of friction that I'd really like to get rid of.
I'm using Arch-packaged Steam, so it's not running in flatpak. I suspect both the headset not detected and desktop view being unavailable issues are Wayland-related, but the Steam Frame itself is running Arch+KDE, and KDE is dropping X11 very soon, so I'm confused that this setup is not functional even in the latest version of SteamVR - it should be what the Frame is running, modulo the CPU architecture.