For years, Apple has muffled PWAs under a pillow. No one knows that you can add them to your homescreen or how that unlocks the possibility of getting push notifications. You also lose any stored data when you go from Safari to an homescreen web app.

I guess this is by intention since with a PWA you would have "near app experience" but for free?

How do you add them? I am using https://actualbudget.org as a Safari page, and it works surprisingly well when "off network" - but a button on the home screen would be nicer.