StarLink is particularly difficult, at least the version I’ve abandoned. They don’t provide a way to wire a product to the router, which is somewhat frustrating. You may want to read the instructions in the new router - installation instructions FAQ.
You didn’t state if these were new devices, or repurposed from your existing system. But you may want to, while you’re setting up the new system, power down your existing WiFi, just so there is no chance for confusion by the Sonos devices.
To be honest, I’d just set up the StarLink with exactly the same SSID as your home network, and just power it down when you’re parked at home, and let the RV speakers automatically connect to your home network, then switch to the StarLink when you’re away from home. That way you can ‘manage’ your Sonos from home, but have them connect to the powered on StarLink when you’re away.
