Perhaps you haven’t been paying attention but macOS Sonoma—currently in beta, shipping this fall—has the best web app support we’ve seen in a mainstream operating system.
You can put a web app on the Dock using the Finder’s “Save to Dock” command for virtually any website or web app.
Not only do you get service workers, push notification, web app manifest support, etc. web apps have first class support in the Finder, Spotlight, Spaces, Mission Control, etc. [1].
[1]: https://developer.apple.com/videos/play/wwdc2023/10120/