Those are useful links but are they don't give PWA's the same rights as native apps.
Chrome apps do use HTML and JavaScript but aren't PWA's. The API's and sandboxing is different.
There are many useful HTML5 API's, but they don't require code signing as far as I know, and they don't have the same permissions as Android apps. (The permission system is entirely different.)
You are missing an important thing on how PWA are supposed to be coded.
PWAs are supposed to check the avaialbe sandbox APIs and adapt accordingly.
So if a PWA is running on Windows on an UWP context, it can check it and then access UWP APIs, if they are running on Chrome OS instead, then check accordingly and act upon it.
Finally if only play old HTML 5 APIs are available, then make the best of it.
That is the whole point of Progressive, to enhance the experience depending on the surrounding context.
I thought the point of PWA would be ‘free’ compatibility with every OS that can run PWA. Checking for several different APIs and using the appropriate one seems counter to this.
https://developer.chrome.com/apps/api_index
As for Android, the "What Web Can Do" PWA displays what extensions are currently available, https://whatwebcando.today/