By default Moodle keeps logs forever which causes the database table to grow. In my experience you don't need to keep logs for more than one year but you need to decide this (your organisation may have a records retention policy). You can change this in Keep logs for under Site administration ► Plugins ► Logging ► Standard log.
But if there are lots of old entries removing these can take (many) days. They're removed by the cron, it deletes as many old rows as it can for five minutes every day.
So it might be easier to remove these from the database table directly. E.g. to delete log entries older than a year:
=# DELETE FROM mdl_logstore_standard_log WHERE timecreated < EXTRACT(EPOCH FROM TIMESTAMP '2019-08-21');
Ensure you have a backup of the database before making changes like this.
This is a PostgreSQL error so increasing max_execution_time won't fix this. You can check what this is set to in the PostgreSQL shell with SHOW statement_timeout.
=# SHOW statement_timeout;
statement_timeout
-------------------
0
I think this is 0 (i.e. no limit) by default so maybe it's been enabled on your system? You can change this in postgresql.conf but it will affect other users and databases if Moodle isn't the only database on the database server.
