@neil I think the main reason this might not be obvious from the documentation is because the idea of a 'server' doesn't really make sense in Syncthing's model. If you just share a folder from one central device that's always on, you get a traditional hub-spoke model no matter how many other devices you share it with.
You might want to consider setting that 'server' up as an introducer, that way all the devices you share a folder with will also automatically connect to each other, so they can sync without the server in-between.
For added security you could also consider setting a password on it and making the server untrusted, that way the server never decrypts the data but can sync with all devices.