It does not, and that fact is the #1 downside of Postgres. It is not predictable or controllable at scale, and comes with inherent risk because you cannot “lock into” a good query plan. I have been paged at 3 am a few times because Postgres decided it didn’t like a perfectly reasonable index anymore and wanted to try a full table scan instead :(

Nope, weirdly Postgres still doesn't have that ability even today.

It’s not in core, but there are multiple extensions that provide this functionality