A future iOS update is bringing cool new features to Safari. These features will make web apps that are saved as icons to the home screen function more like regular apps. They will be able to show notification badges and even push notifications to the lock screen.
There are some good updates coming for third-party browsers too. Very cool.
Web Push for Web Apps on iOS and iPadOS | WebKit
Now with iOS and iPadOS 16.4 beta 1, we are adding support for Web Push to Home Screen web apps. Web Push makes it possible for web developers to send push notifications to their users through the use of Push API, Notifications API, and Service Workers all working together.
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 — such as tapping on a ‘subscribe’ button provided by the web app. iOS or iPadOS will prompt the user to give the web app permission to send notifications. The user can then manage those permissions per web app in Notifications Settings — just like any other app on iPhone and iPad.
The notifications from web apps work exactly like notifications from other apps. They show on the Lock Screen, in Notification Center, and on a paired Apple Watch.