It the Oculus version and yes am starting it from the Game TAB
It got be started from the game tab as it not available as Quest software..
I know it's not on the Quest. But, do you know you can start the Oculus PC software and Steam VR from inside virtual desktop?
The reason I asked was it the Oculus Version or the Steam Version is that Steam sometimes defaults to theatre mode when starting some VR games/experiences. It's exactly what you describe, a big 2D screen.
And No, you don't need the Sidequest App anymore for Virtual Desktop. But, SideQuest might be worth installing and trying out anyway as there are some nice games/experiences available.