Authors have to submit manuscripts to publishers individually (or, in some markets, agents who work with multiple publishers in the same niche).

Publishers get showered with manuscripts. Very small percentage of them are what publishers deem will meet market goals.

In standard publishing contracts, the author gets paid an advance. This is basically the royalty percentage for the entire first print run. It’s not refundable. It represents the trust the publisher puts on the author, and if the publisher can’t sell all copies, well, tough for them. (They’d probably just not work with that author again.)

Getting to that point is a pretty massive hurdle to clear for first time authors.

So no, authors don’t really get to pick their publishers. The only scenario where people get to pick their publishers is some celebrity deal bullshit.