If PostgreSQL has replication, why are they talking about "minimal" downtime? Is there no quorum strategy that delivers high availability? I don't know as much as I should.
Writes happen on your primary. At some point, you need to stop accepting writes, wait for the replica to fully catch up, reverse the replication so the replica is the new primary, then direct writes to the new primary. That's hard to do without any downtime.
There's no option where the nodes all accept writes.
That still only has one primary: you can't just start pointing writes at the upgraded standbys. Synchronous replication (besides having its own downsides) just shortens the time needed for the replicas to catch up. You still need to perform a cutover.