What are all these Google internet hosts (domains) and why is stripped-down Android connecting to all of them?
I don't know the purpose of all hosts, but here is what I know:
connectivitycheck.gstatic.com
On this host typically only the URL https://connectivitycheck.gstatic.com/generate_204 is used. It is used by the Android device to determine if there is Internet access or not.
android.clients.google.com
Primarily this host serves Google Play Store for all sorts of queries, e.g. search for apps, periodical device registration, ...
history.google.com
The purpose of this host is not quite clear. The used service is called &quot;history recording&quot; and the server responds if it should be enabled or not. Potentially this is the host for the Google location history recording?
play.googleapis.com
Obviously this API is used by Google Play Store. For example if an app should be downloaded this server is used (besides some other servers).
android.googleapis.com
As far as I know this server is used for authentication purposes and for Google push notifications.
www.googleapis.com
Used by various Google services such as Google Calendar, Drive, Chat, Hangouts, User Location, Android Video ...
Inspect the traffic on your own
If you are interested in more details and have a rooted spare device I recommend to you to install Xposed + TrustMeAlready plugin (this disables SSL/TLS server check for every app - hence makes SSL/TLS totally insecure therefore don't use this on a regular device). Then install an HTTPS intercepting proxy such as Fiddler/Mitmproxy/Charles, ... on your PC and configure your PC as proxy in Wifi settings. Afterwards you can see all the data transmitted by your device.