Why does pg_last_xact_replay_timestamp() sometimes return extremely old timestamps?
Answering this from the future - when I have seen this, it means there have not been any writes to the primary (upstream) database in a while.
If there are no recent transactions on the primary, there are no recent transactions to replay on the follower, so pg_last_xact_replay_timestamp() will just report the time of the last write to primary.