In Apple parlance I believe they call it the action button not the share button. If understood that way adding to Home Screen is easy to find. The fact that so many people on HN keep calling it the share button means that Apple hasn’t communicated the concept very well.

I Google "ios action button" and find nothing. I google "ios share button" and screens full of the button we're talking about. So regardless of "Apple parlance", this is the "share button".

Is it harder than clicking on App Store icon?

Especially if you put a nice large animated instruction right on the web page.

Yes, it's way harder because "share" is semantically incompatible with installing an app.

But, less hard than dragging a CD/DVD to the trash can to eject it.

Even less hard than writing machine code in binary.