Is HTTPS not secure channel for communication between client-server? What is the reason behind using an entirely different protocol for client-server communication[0] over HTTP?
No, you don't. Use a self-signed certificate that is hardcoded in the app.
Also, I think App Store software delivery doesn't depend on only TLS, but also on Apple's signature. And you can visually verify that the source code downloaded from GitHub doesn't contain backdoors.