There are definitely more rooms in the Scion HQ than we have access to. From recent patches we know that the door near Tataru's desk leads to the infirmary, and I expect there are other rooms available - maybe more of a communal bunk room than individual apartments. (I can't remember if there are other visible doors at the Rising Stones, but it's always possible that there are corridors that we don't see.)

Or some of the Scions might be living elsewhere in Revenant's Toll.

Beyond that, the main Scions stationed in the city-states might all have permanent rooms at the local inns - a good place to pick up information and keep track of what's going on. Momodi, at least, is a "good friend and ally" of the Scions, and I'd expect the other innkeepers might be the same.