According to this, notifications are possible if you add the app to the home screen, which I didn't know.

A feature more devs should use- I've been surprised how much websites behave like native apps if you just "add to homescreen" instead of downloading an official app, e.g. twitter, instagram.

When you open the shortcut, it doesn't launch as a tab in safari, but appears independently in the app switcher. They are often indistinguishable from official apps!

Seems like a great way for devs to avoid app store pains