Diagnosis
The Nest system has lost its connection to Google's cloud services, but your local network is still functioning. This is a common cloud sync glitch.
How to Fix It
Reboot your primary Nest WiFi Router. Unplug it, wait 30 seconds, and plug it back in. Give it 5 minutes to fully reboot and re-establish the cloud connection. The app status should update.
If That Didn't Work
The issue might be with the app's cache. Force close the Google Home app, clear its cache (in your phone's app settings), then reopen it and pull down to refresh the home view.
Heads Up
As long as your devices have internet, this is an app/cloud display bug, not a network failure. You can't change settings while it shows "offline," but surfing and streaming will work normally.