On iOS, I have several ways to know when the user launched my app from the home screen when the app was backgrounded:
Is there an equivalent in WatchKit? If not, are there any robust alternatives?
The closest you'll find with a WatchKit extension is this set of notifications that were introduced in iOS 8.2:
NSExtensionHostWillEnterForegroundNotification
NSExtensionHostDidEnterBackgroundNotification
NSExtensionHostWillResignActiveNotification
NSExtensionHostDidBecomeActiveNotification
You can read more about these notifications in the NSExtensionContext documentation.