Mediamtx will receive video from the camera using whatever protocol the camera supports and make it accessible over HTTP.
Make sure if you’re using an infinite file HTTP stream instead of DASH or HLS that you configure the timeouts on the reverse proxy appropriately or else your proxy might interrupt the video after some number of seconds. I’ve wasted a lot of troubleshooting time on proxy misconfiguration like that.
Does Syncthing actually work with device IDs? It seems to work with encryption keys which should be stored in the user directory, at least if Syncthing is running as a user. Is the problem just that you have two machines with the same name in the same network? You can change the name.