Hell yea my site works cross-browser. I've tested it with Firefox, Chromium, Midori, w3m, lynx, surf, and edbrowse and they all look fine.
I freely admit I have no idea what a PWA actually is, but that page is not helping me understand. All I find are vague descriptions about how they're reliable, fast and engaging, but nothing even approaching a definition. For all I know, a 16-ounce claw hammer is a PWA. It's certainly very reliable, fast and supremely engaging.
If PWA is all about the service worker, why are things like HTTPS, splash pages, 200 offline, or address bar matching brand colors(?!) included in the category? Those things don't make my site any faster or more responsive, and I doubt a service worker would either. Why on earth would I want my site to return 200 offline anyway? I don't wanna lie to a user.
Ok, lemme take a deep breath. I'm sure a PWA does not equal a single-page broken piece of JS monstrosity. I just don't think it's a good idea to give me bright red warning triangles about not having a service worker unless Google believe every site should have a service worker. In that case I disagree with them because I don't think I need a 200 OK if my network interface has caught fire in the middle of browsing.