It is the same as having shared GTK or QT libraries (both with embedded web engine BTW - so plenty of engines already), or having a shared global python deployment with shared global packages (from these you sometimes need two: v2 and v3)
So you will have one extra component per system.
In Windows world maybe you will have one additional electron component per app, but there, it is the "normal" way (you have qt dlls in every qt app etc...) anyway, so not much difference compared to other frameworks there too.
Also, the platform for a PWA gets upgraded more regularly, which can be good (security patches or bad (breakage).
On Windows(UWP) and ChromeOS/Android, PWAs have the same rights as other apps if properly signed.
I don't know about Android / ChromeOS.
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/
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.)
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.
Browser specific APIs are a thing since the Web became a platform instead of plain hypertext documents.