Share is the button to bring up the menu with myriad actions like bookmarking, adding to reading list, printing, running third party actions, etc. Has been for years. Obvious? Maybe not. Obscure? Also no. There are very few buttons you can click to begin with: it has to be either AA or Share.
Oh, and you omitted that you need to scroll down the share popup. A popup that primes you as scrollable sideways, don't forget.
When my family was discussing getting an older member a smartphone, I briefly thought about it and realized that the whole lore of what's srollable would be impossible to explain. If you don't want a feature used, put it "below the fold" in a popup.
It’s a pretty clunky call to action, though. The simplest thing for the user would be a button right in the message telling you a PWA is available. “Tap here to install” and it’s done.
Instead, you need to tell users “Hey, we have an app! No no stop, wait, don’t go looking in the App Store it’s not there. Instead you need to hit the share icon. Yeah it looks like a box with an arrow coming out of it, down the bottom of the screen. Yeah if it’s not showing you need to tap the gray bar at the bottom first. Then the share button. Then look through for something that says install to Home Screen. Yeah scroll down a bit and maybe scroll across until you see it. Yeah there you go.”
True. The context of this thread is discussing the process on iOS, and the hypothesis that it leads to lower adoption of PWAs on Apple's platforms. From the original comment:
> > Apple said PWAs had "very low user adoption"
> Installing PWA isn't obvious for users on iOS Safari or even macOS Safari. It's very obscure
Doesn't seem that obscure and for me the issue is much more with websites not making it clear when a PWA version of the site is available.