Comment by littlecranky67

Push notifications work anytime, even when your phone is locked and in your pocket. On iOS you need to add the website "to your home screen", which then it becomes like an App (it is a progressive web app, PWA). For Chrome and Safari on Desktop it is the same (you even get notifications when your laptop is locked on macOS, provided you configured that in your settings of macOS).

Source: I run a PWA that enables web push (without any 3rd party push services) and have tested it many times on many platforms, and my users use them too.