straight to the question/story: I've working on a progressive web app for some weeks. Despite the fact that the PWA support on iOS/Safari is limited, my PWA works quiet well on Apple devices too.
Unfortunately I fooled myself by thinking that Safari on iOS contains the same feature set as Safari on macOS. More to the point, I realized too late that Safari on iOS are not capable of receiving push notification by Apple's push service.
So I thought about alternatives. The first thing that came to my mind was a combination of Websockets and a Service Worker to receive background messages. But I cannot find any method to make the user aware of those messages, when the PWA is running in background. I consulted books, documentations and of course Stack Overflow. Because of the missing Push API in Safari I cannot create a notification, the Badge API (https://wicg.github.io/badging/) is an early draft and I doubt it will directly implement into Safari as soon as it is defined.
Maybe some iOS/Safari-Guru has a suggestion to notify my users about new messages.