We are in the process of upgrading our PostgreSQL database from version 12 to version 15. I would greatly appreciate your advice on the following:
1. Would it be recommended to use the --link option with the pg_upgrade command, from disk space point of view?
Yes.
Are there any potential downsides to consider?
Very much: it's a one-way journey. No rolling back if something goes wrong!
2. Do you have any suggestions or best practices for performing an efficient upgrade in a replication setup (streaming replication) for both the primary and standby servers?
Streaming replication is not an upgrade method. Logical replication is absolutely a valid method of upgrading PG on one server to PG on a different server.