How much space does a queen really need?

Depends on how fast she is laying eggs!
Here is a visual representation of how much area a queen can fill depending on her egg laying rate, and depending on what kind of hive she is in.
[ ] 1st week of brood development, 3 days of eggs, then 4 of the days as larvae;
[ ] 2nd week, 2 days of larvae, then the rest as capped brood;
[ ] 3rd week, 7 more days as capped brood, emerging on the final day.
[ ] Honey is on the outside edges of the brood nest, no brood there in this model.

Note that by the end of the 3rd week, the brood is emerging and leaving an open space for the queen. So she could just go back to that open comb, rather than move elsewhere to lay eggs.

That is why the brood just cycles between the 3 colors: the queen can cycle through that volume as long as she is laying at that egg rate.