This answer seems to imply that “palazzo” is a very grand luxury building, when in fact (in addition to “palace”) it means simply any large building - often typically a standard multi-family apartment building.
I think here palazzo is used for ironic emphasis, it sounds so much better to say palazzo than reggia. When I commented on my friends big house in Lucca compared with my modest apartment, she exclaimed, “Oh yes, I live in a real palazzo no!”