I don’t believe he will be at Castel Gandolfo after he retires. He won’t be pope anymore, so he has no right to be there.
The Pope Emeritus is retired, he is at the Castel Gandolfo.
The Vatican is letting him stay there until Mater Ecclesiae is finished, which is only a few months away.
I doubt very much the new Pope will throw him out in the meantime.
After seeing him today, we can’t even be sure he’ll live long enough to move into Mater Ecclesiae...