Postgresql pg_cron job never executed
The tasks initiated by pg_cron must be able to connect with the
parameters mentioned in cron.job, without a password.

If steps have not been taken in pg_hba.conf or through a .pgpass file
in the server's environment to allow for that, the task won't be able to run.

Concerning the log file, error reports would be expected there, but
pg_cron logs at the LOG level. Maybe it's below your current level
(see log_min_messages) or there's another problem.