When you signin with Google in an app having Google device registration enabled on microG (disabled by default), Google gets your IP, the account you entered and the app you signed in to. The rest is randomized.
When you enable Google Cloud Messaging (disabled by default), then Google gets, with every push message, your IP, the service associated (app) and, depending on how push messaging is implemented in the app, then some other data than could serve to stablish relations.
AFAIK, no more information is shared with Gobble. If any, then it won’t be enabled by default surely. Every other service in microG is implemented with OS services (maps with OpenStreetMap, network location with the backend you choose).