In the meantime, if you really need it, have a look at this project: https://github.com/khmyznikov/ios-pwa-wrap
It's a iOS PWA template that uses push notifications via Firebase.
Capacitor can be added to an existing web app codebase and acts as a library with cross-platform APIs for functionality like Camera/etc and that would be compiled/linked into your app like any JS library. But it can also be used to wrap an externally hosted app by changing the server.url config value https://capacitorjs.com/docs/config
We provide push notifications along with a few more important things that you'd need to wrap your web-app with.
Full disclosure: I'm its founder and you can reach me on marvin@goose.red.
Google and Mozilla have supported the web push API for going on 6 to 7+ years now.
https://9to5google.com/2021/10/10/google-ios-apps-native/
Facebook realized years ago that true native apps and not a web wrapper was a better user experience.
Given the choice, I'd use Facebook messenger in my phone's web browser but they block it.
I don't agree that a native app is a better experience, as it gives less control to me the user.
Maybe it's a better experience for product managers who want to increase my engagement and collect as much information on me as possible.
[0] Ask someone who worked with computers in the late 90s and 2000s if you don't get the reference.
We work with Google -- and even sync with them monthly -- on this platform. They are very cooperative and helpful.
And, PWAs published to Google Play can do push notifications and anything else PWAs normally do, using just standards-based code.