...with a block saying "VaM" and "Up next" below it. Unfortunately I couldn't get further than that...
No need to add it to your Steam Library at all.
But let me ask a question again: how long did you wait when you got the "Up next" screen for VaM...?! Because VaM can take quite some time (up to several minutes!) to start, especially if you already have installed a couple of addons like scenes, looks etc. -- and it gets even worse if VaM is installed on a HDD (instead of of a SDD/NVMe).
So please try it again: first time without using SteamVR and using the "VaM (
Desktop Mode).bat" file to run the Desktop mode of VaM. Use a timer to see how long it takes to start. Then quit VaM, start SteamVR,
wait until SteamVR is fully loaded, and this time use the "VaM (OpenVR).bat" file to start VaM in VR mode -- then
wait at least twice as long as it took VaM to start in Desktop mode (this isn't usually twice as long, but just to be safe!).
If that doesn't work, I'm out of ideas. Maybe someone else will jump in who actually knows how to run VaM on your Quest 3 headset... At least I tried ;-)
// EDIT: I highly suggest to test a clean, unmodified (as in "freshly downloaded, no additional addons installed") version of VaM first to figure out the steps you need to do to run VaM in VR mode on your headset. Once you've figured it out, you can switch back to an already modified version and try again.