cannot promote after recovery for PITR

I'm running 12.5, I've restored a backup copy (from barman) to a
specific restore point.
The system has gone into pause, and I've checked that everything is as
I was expecting.
Now I'm unable to promote the cluster:

testdb=# SELECT pg_is_wal_replay_paused();
pg_is_wal_replay_paused
-------------------------
t
(1 row)

testdb=# select pg_promote( true, 120 );
WARNING: server did not promote within 120 seconds
pg_promote
------------
f

and the only thing I've got into the logs is

WARNING: server did not promote within 120 seconds

Similarly, I cannot promote via pg_ctl even if I've checked that
PGDATA/promote is there.

If, instead, I do pg_wal_replay_resume(), the server is promoted (of
course not at the PITR I want).
Am I missing something?

Thanks,
Luca