Are you sure? Go to https://sindresorhus.com/screenfull/, tap "Request", and you should see a full-screen website. Any [website|webapp|PWA] can do this with Safari. (Screenshot: https://imgur.com/a/CTWFPol) Third-party browsers using their own browser engines can do whatever they like.
> How do you expect them to make push notifications work with PWAs?
Third-party browsers using their own browser engine will have to create their own support for web notifications, just as Apple does for Safari. Presumably, they'll leverage the same infrastructure they use on non-iOS platforms.