A Quest 2 wouldn't have the power to run a VR app and floating window; it has a hard enough time trying to run a browser and flat game just from Home with virtual environment: https://www.youtube.com/watch?v=BPmphsTu0U4
I’ve heard Discord pings in the background when playing a game so that implies to me that the browser is still running but hidden, so it seems to be possible. I could be wrong here, maybe it did that some other way, but even then it’s probably possible to improve the situation by letting VR games mark themselves as lightweight enough to not need all the hardware or something like that