I'll answer my own question. It turns out the solution is quite simple 😏. To fix this error, you need to reduce the size of the App Clip to less than 15 MB (I managed to do this by adding the -Osize parameter to the Swift compiler settings) and rebuild it for iOS 16. This is actually mentioned in the official documentation: https://developer.apple.com/documentation/appclip/choosing-the-right-functionality-for-your-app-clip