The only difference is that the Galaxy Wearable app probably utilizes Android’s APIs for notifications, which allow it to make use of battery saving features and such.
I don’t disagree that the Wyze app needs work. Part of the problem is that they aren’t properly using the android APIs which is why you get the “app is running in the background” notification.
However, there is no framework for a smart watch to get notifications without an app pushing them to it. They’re just doing it more efficiently/properly. A big step toward that would be spinning up a service/daemon for the notifications rather than having that functionality in the main app directly.