Still, it seems that the current API couldn't really support that use-case if tabs with active audio or video can't be hidden. At least there will be some random tabs hanging around that don't belong to your group.
But the main use-case for this API seems to be organizing things - and it's strange that I would want certain tabs not take part in my organisation scheme.
If I had virtual desktop support, but certain windows are nevertheless shown on all desktops, that would feel broken, too.
Of course notifying users of audio/video recording is important, but this could be done with a separate notification - with options to stop recording or activate and un-hide the tab.
I don't know if this is the case, but the API ought to also let you kill any active video or audio streams playing in a tab. Then you'd be able to go ahead with hiding them.
If this is not possible or planned, it feels kind of broken in my view.