This blog post by Victor Berger explains how to use many of the tools listed on this page: https://levans.fr/shrink-synapse-database.html
The purge remote media API allows server admins to purge old cached remote media.
This API deletes the local media from the disk of your own server.
The purge history API allows server admins to purge historic events from their database, reclaiming disk space.
Tool for compressing (deduplicating)
Some easy SQL that reports useful stats about your Synapse database.