It has been reported that using PostgreSQL and trying to publish any high amount of data/number of sites or pages will make the toast table increase in size up to occupying the whole available DB.

This issue has been reported on PostgreSQL 11.9 when the user tried to publish 8000 sites and ended up filling 15GB of DB available size when trying to publish 120MB of data.

You can find the used configuration parameters attached to this ticket.

There are some workarounds that can be used, like performing an export/import of the data for a first heavy load publication instead of performing a normal publish, executing a vacuum of the toast table after the publish or directly increasing the DB size so it's not filled during the publication.