Is it possible for developers to block their Google Play apps to be installed at AVD or am I just picking the unsupported AVD profile? I'm trying to install the app into the AVD and debug in a more controlled environment, however, it says:
Your device isn't compatible with this version
So, it isn't an error message. It's a Google Play message before installing the app.
There are multiple ways to detect if an app is running on an emulator. But in your case it seems to be a general problem because the error already occurs on installation:
Emulators are usually x86 devices because of emulation speed (as PCs usually have x86 based CPUs). The number of real Android devices with x86 architecture is very very low hence if a developer does not support x86 this can result in an error like you encountered.
Try the latest beta emulators image for Android R it supports both x86 and arm. Therefore on on this emulator image you should be able to at least install the app. If it runs is a different question.
In any way a rooted physical device is usually suited better for an analysis.