What you see on the screen inside wrappers like SyncTrayzor is the Web GUI. You don’t need to set up anything separately if you use those. I think the same is true about Mobius Sync, however being a commercial product you should use their own support channels for any questions specific to it.
When it comes to setting a password up, you don’t need to do it if your GUI address is set to the default 127.0.0.1:8384 addrss, because this way it’s only accessible on the local device. If you want to access Syncthing remotely though (e.g. from another computer), then yes, setting up a username and password is recommended.