I don’t want to synchronize my PC and a laptop directly with each other, but only with the USB stick of the Fritz Box. The advantage would be that you don’t always have to switch on and boot your PC and laptop to synchronize. Does anyone have any instructions on how to do this?
I guess, you need a modyfied* FritzBox first to be able to install syncthing on it.
To my knowledge, no one has ever tried this before 
Copying Syncthing on an USB-Stick and putting it into the Fritzbox will do nothing. The “NAS” service on the FritzBox will only read/write content to that Stick, not start any services or binaries.
*hacked, jailbreaked, dd-wrt’ed, open-wrt’ed, etc. So the *nix on the fritzbox is open and writable.
But maybe I misunderstood you, so please tell us what exactly you want to do/archive.
I found this interesting link: syncthing on a router
Its not solving the problem, just gives some more information on the background…