@Echofox
Google Nest does not make it easy to update Wi-Fi settings for its cameras and doorbells, so their first recommendation is to set the network name (SSID) and password on your new router/modem to the same values used on your old router/ modem.
If you can't do that, then the general procedure is to remove the camera from the Google Home app while you are still on your old Wi-Fi network (which should trigger an automatic factory reset), do a manual factory reset if it wasn't done automatically, and then reinstall it in the Google Home app while on your new Wi-Fi network:
https://support.google.com/googlenest/answer/9223711
