Using a switch to connect Starlink router and Google WiFi router in parallel

How should I connect a Starlink router and a Google Wifi router in parallel (setting aside the possibility that this might be a dumb idea to start with)? In a simple Starlink setup, a POE cable runs from the Starlink POE box into the Starlink router. I want to have the Starlink router active. But I would also like to feed my Google WiFi router (mesh set up to cover my house) in parallel without going through the Starlink router. Conflicts aside, that would give me two networks, access to the Starlink router using the Starlink app and whole house coverage with the Google mesh setup. The Google router has its own power supply. Can I use the Starlink POE output as input into a Netgear switch, perhaps one with both POE and non-POE outputs, that has its own power supply without damaging the switch? I understand I would need POE output from the switch to run to the Starlink router but also (perhaps) a non-POE connection to the Google router. Any help with this question will be hugely appreciated.