By the way, running synapse - docker or not - is a challenge. It can be very complex especially if you are interested in adding gateways to other services and such. Attempting to use https://github.com/spantaleev/matrix-docker-ansible-deploy might be a better choice as even though it is A LOT, it has a ton of good documentation and you can grow with it as it can help you install various different Matrix servers, gateways and clients as well.

Good luck, hope to hear more about how you get on with it.