You have to add the web app to the home screen, then the app needs to ask permission on a click event, the user needs to grant the permission and then focus mode, etc can still filter them out.

In many cases, you have a perfectly functional web app and the only feature you would gain from publishing a native mobile app would be push notifications. Apple used to gate this feature behind its app store/developer program. Now you have an alternative, and I think it was long overdue.