Assuming the stripey white bits are the glass corridors, they still seem to be indoors, so I would call it one building. Certainly it seems more representative of what is there that what was mapped.

Lots of schools have courtyards and fragmented parts.

The green houses can be separate buildings.

leisure=outdoor_seating and leisure=garden are useful for courtyards. It means the area is tagged and doesn't trigger 'unconnected way' or 'area has no tags' issues.