Alright, I have surveyed. The crescent between the northern and southern buildings is indeed an open space, called "Art Garden", still getting set up, hence the entrance from the lower east still being fenced off and signed "construction site". I've separated this structure out into its own, separated the North and South Building respectively into their own building=museum and created an all enclosing tourism=gallery for the primary identity of the gallery as a whole. This seemed better than a site relation, which the wiki mentions to be poorly supported by clients and advised against, if anyhow possible. I would say this is the best solution for now. I'm not certain about the formal extent of land that belongs to the gallery. The geometry defining it is this one: https://www.openstreetmap.org/way/1265404795. Please feel free to update or let me know if it is inaccurate.

If this looks good, shall we close this note for now?