Matrix and its implementations like Synapse have a very intimidating architecture (I'd go as far as to call most of the implementations somewhat overengineered) and the documentation ranges from inconsistent to horrific. I ran into this particular situation myself, Fortunately this particular step you're overthinking it. You can use any random string you want. It doesn't even have to be random, just as long as what you put in the config file matches. It's basically just a temporary admin password.
Matrix was by far the worst thing I've ever tried to self-host. It's a hot mess. Good luck, I think you're close to the finish line.
funnily there's an.. ansible i think? project that makes selfhosting synapse easy as fuck, you basically just go "ansible deploy synapse" or whatever the syntax is and it does almost everything for you.
Matrix seemed interesting right until I got to self hosting it. Then, getting to know it from up close, and the absolute trainwreck that the protocol is, made me love XMPP. Matrix has no excuse for being so messy and fragile at this point. You do you, but I decided that it isn't worth my sysadmin time (especially when something like ejabberd is practically fire and forget).
I still have to sort out having a different server name to the access name so I can use the domain as well. Do I just put a field into the config like the rest? Can it go anywhere?
You just need to figure out how many miliseconds since the unix epoch the media you want to purge was uploaded, and then offset the time to only purge that old or older.