I believe app.getSharedData global variable will be available anywhere in the app only when you load it through Application OnStart event. If you change this variable in the App page then it will be only available within that page. It will not be available in the another form.
So in summary, the variable defined at Application onStart is global, i.e. accessible from all appPages and Forms within the app itself.
Should the value of this variable be changed by JavaScript by either a Form or an appPage within the app, the 'new' value is only present in memory / runtime. Navigating to another form or appPage within the app will result in this value being 'lost' and any any future reference to the global app will revert to the original Application onStart value.