[Code health] Design flaw in main startup flow

Play services and login are tied to an event triggered by `MainViewModel` and handled by `MainActivity`. The `MainActivity` may not be active when this event is triggered, so it will sometimes miss the sign-in event, for example when the app is temporarily in the background (e.g., when Play services are being installed, and when started in the background while debugging from Android Studio).

The initialization flow "evolved" while we were still learning modern Android dev, rather than being thoughtfully designed. @shobhitagarwal1612 @scolsen @anandwana001, any ideas on how this should work in practice?