So you added the secret to the file and restarted the docker container, right?
Something that I think will help you with self-hosting in the future is to always read through the entire process for setting up whatever you want to set up first, beginning to end, so that you are familiar with what you need to do before attempting it the first time. It's helped me numerous times myself.
Which config file does it go in? Where does it go in that file? Do you literally just put "registration_shared_secret" or does it need a value? What is the syntax of setting the value? Does it accept spaces, special characters, etc.?
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.