Sending push notifications to iOS without relying on a native app has already become a mature option. Last year Apple extended the standard Web Push with Declarative Web Push, which finally makes the whole thing make sense. (It's handled natively by WebKit rather than driven by JavaScript, which improves push reliability and privacy, much like the native push notification model.)

Kukuroo uses Cloudflare Workers so that end devices can subscribe to push notifications and relay push requests to the Worker, which signs and delivers them. I personally found it genuinely useful and full of potential, so I open sourced it: kukuroo.cc

Requirements:

Safari on iOS and macOS only (though seriously, who receives push notifications on macOS?) The web page that receives the notifications has to be added to the Home Screen A Cloudflare account. Push notifications and lightweight serverless functions are a perfect match

The might have fixed some issues but the fact that it is only available for homescreen websites and that the link to add them there is buried in the UI is very stupid imho.