Matrix isn't exactly a privacy-respecting service. Its goals are propagating data across multiple servers, linking and duplicating it to third parties like Discord and Slack and Facebook, and keeping it intact.
Right now, if you request a GDPR compliant data deletion, they won't delete any messages you've sent*, and "your username will continue to be publicly associated with rooms in which you have participated."
* messages intentionally remain on the server until housekeeping functions kick in, which is true for any account... But those functions only clear rooms that have no participants at all.