Apartments aren't land, they're buildings. Buildings can be made arbitrarily tall; if we built tall buildings we'd have more housing units than people long before we ran out of land.
So if there is a machine that can build buildings for free, apartments should be cheap. If there isn't a machine that can build buildings for free, get a job building buildings for money.
Even if 100% automated, there might still be a residual cost to building as it needs energy (assuming than raw material is free). I do not think that because the building would be not free, it would allow human to compete (too slow, inaccurate, etc.)
Delivery should be automated.
Rent would obviously crater as building housing craters too (robots making it, materials being extracted and manufactured by robots too). But again, it would still cost something (energy at very least and assuming energy is not free).
So I suspect that even if 100% is automated, we would still need little money to pay for the basics (food, shelter).
And that's the point. The problem isn't caused by automation, it's caused by zoning restrictions.
Like sure all the goods are stupid cheap but things that are actually naturally rivalrous and exclusive like real estate continue to hold value most random people are pretty fucked it seems.