I would stick to using Apple Apps (and yes, [Apple uses http for delivery](https://apple.stackexchange.com/a/448111/5472) - [content caching on macOS][1] will show you the requests easier than using a proxy on your iPhone or intercepting the traffic on the network. The benefit of caching service is additional logs / and cache the files will be present on your Mac hard drive when any iOS device on your subnet downloads the app).

If you manage to fake out the store with a web browser that mimics the app request - consider what a terms of service / license violation would entail. 

> - Manipulating play counts, downloads, ratings, or reviews via any means — such as (i) using a bot, script, or automated process

> - You may access our Services only using Apple’s software, and may not modify or use modified versions of such software.

https://www.apple.com/legal/internet-services/itunes/

Once you’ve downloaded the app using Apple’s software you should be clear to analyze it as long as you’re not further distributing it or using the app should you choose to alter or change it and not just learning how it was assembled. Consider checking with a lawyer in your area if you have questions on contracts/licensing questions. 


  [1]: https://support.apple.com/guide/mac-help/what-is-content-caching-on-mac-mchl9388ba1b/mac