So what about a race condition, stale blocks? What happens if two miners find two blocks of the same height and broadcast them almost at the same time? One of those blocks will become stale, but before that happens, who is making those mempool blocks?
Same as always, the longest chain wins.
That's not what I'm talking about. I'm talking about the ~10 minutes in which there are two longest chains because a block has not been found yet that builds on either of the two competing blocks.