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

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.

There is no purge API for local media because you may be the only one with a copy. If you are sure you want to delete local media you could use something like the following to delete media that hasn't been accessed in a while.

find /path/to/synapse/media_store/local_content -atime +365 -delete
find /path/to/synapse/media_store/local_thumbnails -atime +365 -delete

This will delete media that hasn't been accessed in 365 days.

Warning, check noatime flag: You also have to double-check that the filesystem where synapse's media store don't have noatime flag. Check it with mount, noatime is something that is usually enabled by default to reduce read-write operations in the filesystem for a feature is not so demanded.