Does the iOS/iPadOS version of safari support push api standard with service worker?
iOS 12, 13, and now iOS/iPadOS 14 still doesn't support these features:
So many requests from the community for these features but Apple don't want to hear it. Maybe they think these features have a bigger chance to be unnecessary exploited(spam, etc). And also maybe they want to force developers to create the native application rather than the progressive web application.
I tested iOS 12 in beta last week and as Anand said, there is no change about this functionnality and more globally for Progressive Web App because the Web Manifest, in developpement at this moment is not implemented yet.
iOS don't support the W3C Spec web push notifications yet. But there is a Safari specific API for web notifications. Refer to this answer on multiple options you have.
https://stackoverflow.com/a/49803408/1057093
Update: Corrected the Answer in the above link to clarify proprietary solution is only for OS X - Safari and no solution for iOS Safari yet. Custom in app notification is the best we can do today for iOS Safari.