If you can create a port forward in your router and run stuff at your house what's the point of a relay then? Just expose the ports that Syncthing uses and configure your client to connect to it using your dynamic DNS. No public or private relays are required.
Port forward the following in your router to the local Syncthing host, any client will be able to connect to it directly:
Port 22000/TCP: TCP based sync protocol traffic
Port 22000/UDP: QUIC based sync protocol traffic
Go into the client and edit the home device. Set it to connect using the dynamic DNS directly: