Since I've gone https almost everywhere (thanks, LetsEncrypt.org), my SubFire apps (mobile and the baseline project for the 2.0 suite) are now full-fledged PWAs.
On Chrome for Android (8), "it all works". After a few launches, it prompts to add to the home screen (by virtue of detecting https, service worker, and manifest). In doing, it wraps it up in an instant APK and becomes a full-standing app in your normal app list, tracking its own memory, bandwidth, and cpu usage. Media session api works (but it did in-browser, too). I haven't tried more extensive file caching yet, but I may consider it now. It is tricky - the app has to tell the service worker to cache a file, and then there's the matter of how does one get the streaming URL for the file from the cache rather than loading it by 'fetch'.
We've seen announcements of PWA support in IOS 11.3 (I'll link to a review in the comments), but I wanted to see what the state of PWA support is on other browsers for Android and Windows 10.
Samsung Internet (Android 8) - add to home page will keep the icon (in Android 8, the mini-icon indicating the browser that it will use is there). It will pay attention to the manifest and open 'full screen' if specified. However, the audio tag doesn't work - it keeps skipping to the next song right away, so it isn't getting the right events and I'll need to debug someday. Not a high priority for me.
Firefox Android - finally it pays attention to the manifest, opening full-screen and using the right icon. Android doesn't treat it as a PWA the way Chrome does, in that the icon has the 'opened by Firefox' mini-icon on top. Audio tag behavior is fine. Doesn't support media session API, but it will open normal browser notifications, something Chrome does NOT support (they want you to use push notifications from the service worker instead). This is a lot of progress; even last year, it was still ignoring the manifest and opening within the browser window with all the address bar stuff.
Amazon Silk on FireOS tablets: still no PWA support at all, and no add-to-homescreen feature at all. Everything on your tablet pages have to come from amazon directly so far. Silk does automatically put up a play/pause screen off the notifications bar (like Chrome Android does) so you can pause the audio without having to find the right tab or re-open the browser.
Windows 10 - nothing yet. Chrome add to desktop allows you to say open-as-window, and the service worker can run in the background if you want, but little more. However, I haven't tried it in 'tablet mode' yet. Only uses notifications, not media session api, and only if https.
Edge - nothing yet. Pin to start menu or task bar will just open the page in Edge again. Windows has announced PWA support, even being the first to say they can host in their app store, but it isn't there yet.
Chrome has announced improved PWA support for the other platforms, but nothing yet.