I just accidentally found out the answer to my own question when troubleshooting a different problem. The following isa command works:
It was kind of tricky to figure this out as most of the time class will output something like this that I can use. It doesn't do this in the case of a user made class or App - it returns the name of the custom class or app instead. However, I realized after seeing an error message with matlab.apps.AppBase in it meant the App must be a subclass of the superclass matlab.apps.AppBase, I checked the code in App Designer, and sure enough, every App starts with a line like this:
classdef myApp < matlab.apps.AppBase
I felt a little silly that the answer was that easy to find (if I knew where to look), but this confirms that all Apps are subclasses of matlab.apps.AppBase and therefore you can reliably use that with isa to check if it is an App.