Windows 8.1 (both phone and desktop) briefly supported Live Tiles driven by refresh/pull of a tiny bit of metadata you could easily add to the HEAD section of a webpage. If a user bookmarked that page to their Start Screen, Windows would poll that page every so often (IIRC as often as once every 30 minutes) and the user would see the notification eventually. It was a neat way to run very basic scheduled tasks. [1]

I wish something similar had become more common. I understand why all the platforms are focused on push notifications rather than pull notifications, but it's so much easier to write a bit of HTML/XML templating than to write anything with a PWA ServiceWorker and the Push Notifications API.

[1] The one app I built during that brief time was to poll NaNoWriMo for count API updates. It's a really simple app and was easy to customize with just an old school HTML method="GET" form. https://github.com/WorldMaker/NaNoWriMoAtGlance/