It is absolutely an OS issue, but neither mobile OS has any incentive at all to do anything to make PWA's actually work.

In fact, they have every incentive to make sure they don't work. You can see this in their constant regressions in areas that only actually matter to PWA's.

I will say this: Google has been a lot more fair and open to PWA's and related tech (like WebRTC) than Apple. Apple absolutely hates the idea of any web app that might survive outside of the app store. In fact, for a very, very long time you couldn't even upload a photo on Craigslist with a standard HTML "Browse" button, because "IOS doesn't have a filesystem." It was a conscious decision to not allow the camera to be accessed except from within an IOS app.