“A web app that has been added to the Home Screen can request permission to receive push notifications as long as that request is in response to direct user interaction”
iOS 16.4 lets Home Screen web apps send push notifications, the same Web Push that Safari on macOS got last fall. It only works after a user digs through the Share menu and taps “Add to Home Screen,” and only through Apple’s own push service. Apple counts web apps as a feature while keeping them hidden enough that nobody threatens the App Store cut.