I think it's pretty feasible for a web app (assuming the user trusts it) to prompt a user and explain how to add it to homescreen from iOS Safari. I can imagine, and think I've seen in the past, a nice-enough UI flow to get people to install a PWA. After explaining the benefits, you have an "Add to Home Screen" CTA button. When the user taps that, if it's iOS Safari, you pop up a modal that visually explains the two steps required, which are (1) tapping the button at the bottom of the screen, and (2) tapping the "Add to Home Screen" menu item. (OK they need to do one final tap on 'Add' to confirm the title, but most users who've got this far would manage that on their own.)

I agree that's not as good as a native install prompt but I don't think it's a strange incantation/utterly unintuitive. I know that icon originally meant 'share' but these days it means a wider range of things - basically "take this thing somewhere else".