There seems to be a few misconceptions around what is and what isn't a PWA. A PWA (in my opinion) is simply a website that makes use of certain browser features (e.g. service workers, push notifications, manifests). It's a bad definition, with a lot of grey areas, but it is what it is (and let's face it, definitions in web development are often hard to pin down).

For example, we built https://usebx.com/app with plain old HTML, JavaScript and CSS. Yet, it can be installed on your phone, send you push notifications and even works offline. So I would categorise it as a PWA rather than a website.

My point is, if you're using service workers, you're more a PWA than a standard website.