What information is shared with Cloud Providers (e.g. Google Drive) by Strongbox?

This is up to the cloud provider and how they define the interaction of third party apps with their storage API. In brief this is likely to include your email address or account username, the name of the third party app (in this case Strongbox) and probably data like the current date/time and IP address.

To be very clear, Strongbox will never send any confidential information or your passwords to a cloud provider.