SyncStartupTracker is a helper class that supposedly helps with observing Sync's startup sequence. It's used by some UI code, DiceTurnSyncOnHelper and PeopleHandler. However,
a) its semantics are a bit weird (it says SYNC_STARTUP_COMPLETE as soon as the engine is initialized), and
b) SyncService::GetState() should make this task easy enough without any special helper class.

I'm also not sure whether auth errors are treated consistently: If an auth errors occurs before the engine is initialized, it's considered an error, but if it happens after the engine is initialized, it's success.

So, maybe we can just get rid of the helper class and check GetState() directly instead, or if we decide to keep it, we should at least implement it in terms of GetState().