It seems like that was changed with macOS 15 because it worked perfectly fine before. Anyway, I found a fix.

@Noblauch , @drewster , you can use this endpoint https://itunes.apple.com/lookup?id=APPID, which returns json wiith links to app icon in different sizes.

Hey, I don't think Apple would be much of help here. I have been sitting on this problem for a long time, and I have my own apps too. What I can suggest - have a look at WinWinKit (winwinkit.com) - it is the first referral programs platform for mobile apps, supports iOS & Mac with Native SDK. They are working on a solution that is exactly what you need. And yes, it will use Apple's system for in-app purchases via subscription.