Correct: Mobile data must be on in order to receive Wyze app notifications. I’m not an Android user, so I can’t help with the Android specifics. But I can give you some feedback from the iPhone perspective.
First, I have my mobile data on all the time and it is used by a wide variety of apps. As long as I don’t stream video, I have no trouble staying under 3GB a month.
That said, on iPhone, you can disable mobile data usage on an app-by-app basis. Therefore, you can turn off mobile data for any “data hog” applications and leave it on for lower usage apps. You would then leave mobile data enabled for the Wyze app to get notifications all the time. The Wyze app will use very little mobile data, unless of course you are streaming video from the camera(s) to your phone. In this scenario, you would want to limit live/recorded streaming while on mobile data.
I would assume/hope that Android has similar app-by-app mobile data restriction controls. Unfortunately, I don’t have the Android knowledge to tell you exactly where to find those settings.