[callahad]

> I don't know if that means an Apple server actually listens for the notification from the HTTP server or if the device itself maintains the connection to the server.

In the case of Apple's ecosystem, the device maintains a connection to the Apple Push Notification service (APNs). The website POSTs notifications to APNs, which forwards them on to the user's device. The user's device then wakes up a local Service Worker for that website in order to process the incoming payload and display a notification.

Declarative Web Push makes the very last step unnecessary.

(It's the same on Android but using Firebase Cloud Messaging instead of APNs. Mozilla also runs a push service and its source is at https://github.com/mozilla-services/autopush-rs/)