This blog post by Jackson Chen (Dec 2022) explains how to use many of the tools listed on this page. There is also an earlier blog by Victor Berger (June 2020), though this may be outdated in places.
List of useful tools and scripts for maintenance Synapse database:
Purge Remote Media API
The purge remote media API allows server admins to purge old cached remote media.
Purge Local Media API
This API deletes the local media from the disk of your own server.
Purge History API
The purge history API allows server admins to purge historic events from their database, reclaiming disk space.
synapse-compress-state
Tool for compressing (deduplicating) state_groups_state
table.
SQL for analyzing Synapse PostgreSQL database stats
Some easy SQL that reports useful stats about your Synapse database.