So, what are the lines I need to add to my docker-compose.yaml ;)

This was deliberately the Debian package flavoured installation. We'll probably do a Docker one too (which will likely be a lot faster, but also a lot more mysterious as to what's actually going on :)

Docker would be nice indeed, an helm chart would be even more convenient.

To be clear - Docker & Helm installations of course exist for Synapse:

* https://github.com/matrix-org/synapse/blob/master/INSTALL.md... is the official Docker instructions

* https://github.com/dacruz21/matrix-chart is a Helm one

etc