PostgreSQL template works fine.

Steps to reproduce:

Item key in template

pgsql.custom.query["\{$PG.URI}","\{$PG.USER}","\{$PG.PASSWORD}","\{$PG.DATABASE}","all_tables_stat"]

 
/etc/zabbix/zabbix_agent2.conf

 
Custom script permissions and location

 
/var/log/zabbix/zabbix_agent2.log
[PostgreSQL] Cannot fetch data: query "all_tables_stat" not found.