How to check if a PostgreSQL streaming replicate server is up-to-date with the primary

On the primary, run

SELECT pg_current_wal_lsn(); -- On the primary

In my case, the result was

 pg_current_wal_lsn
--------------------
 0/E015420

On the standby, run

SELECT pg_last_wal_replay_lsn();

In my case, the result was

pg_last_wal_replay_lsn
------------------------
 0/E015420

This means that

All WAL records have been received

All WAL recores have been replayed (not just flushed) on the standby

There is no lag between primary and standby