Exhibit A: In Safari I had to "share" this page to use the "Find on Page" feature to search whether anyone had mentioned the share button yet. Bonkers.
You can also long-press on the address bar to see a whole slew of even more hidden functionality
(seriously though, thanks).
1. tap three dots
2. tap "Share"
3. tap "More"
4. scroll down
5. tap "Add page to home screen"
6. tap "Add to home screen"
other than that apple really doesn't want you to do this because they loathe PWAs and their entire services business model is built around the app store being the sole place of app distribution
Feels like this could be a riff on Android's 'Share' functionality, which is actually the user-friendly name for "send an Intent". And that means that any inter-app handling ends up stuffed into a "Share" menu that pretends only social media apps exist. So you do "Share -> Edit with Photoshop" or similar.
Or type your search in the address bar, scroll to the bottom to the "On this page Find ..." functionality.
A rare example of two different ways to do the same thing on iPhone