The major support for PWAs for Edge was released in this recent Windows 10 April Release.
That also includes Microsoft Store support for PWA apps.
Several applications in the Microsoft Store for Windows 10 have already launched or switched to PWAs (one of the most noticeable one was Twitter replaced their increasingly outdated Windows 8 application with a PWA as soon as the April Release happened).
The Android Store also supports PWAs directly in recent versions (the "Twitter Lite" application on Android is the same PWA that Windows users now get by default, and presumably will be the only first party Android Twitter client once usage of PWA-capable versions of Android rises).
Microsoft's Bing crawler is supposed to start adding "high quality" PWAs directly to the Microsoft Store as soon as it finds them on the web and minimally vets them (and will provide tools to PWA website owners to control/enhance their listings).
Google's search crawler team is also supposedly investigating lighting up automatic app ingestion into the Android and/or Chrome Stores.
