Two (very quick) minutes on their GitHub repo and it's pretty obvious that they're using firebase-analytics and at the very least seem to be sending URLs[1] and infos such as the model you download or the capacities[2] you use.
[1] https://github.com/google-ai-edge/gallery/blob/main/Android/...
[2] https://github.com/google-ai-edge/gallery/blob/main/Android/...
That’s not the same app as posted which is for iOS.
You're right, they reference IOS in the README.md and link to the GitHub repo from the Apple Store page yet don't include the IOS source, sneaky.