Its quite easy to selfhost. They now even provide an installer script that helps with setup and updates. But it consists of multiple service to host the full stack. A bit more than you would need to run a fully featured Synapse(PostgreSQL, Livekit, etc.). But still not as heavy on resources as Synapse, i guess mainly because matrixs federation needs a lot of resources.

Synapse is made by a corporation(Element) and not the Matrix foundation anymore. Also Claude is amongst the commiters on the git repository…

If i get the license right, this doesn’t really qualify as open source. Its source available.