Please mind that "Browsers that support Progressive Web Apps" is not a real term, PWA itself is a set of features that a web app can provide for users. So it's not just only about Service Worker and App Manifest.
Check out: Baseline PWA Checklist.
Here are what you can do to achieve PWA on iOS/Safari at the moment this answer is created:
- Site is served over HTTPS ✅
- Pages are responsive on tablets & mobile devices ✅
- The start URL (at least) loads while offline
