service-worker-caching-does-not-enable-web-push
A sw.js file with network-first fetch caching is not a push notification system. Real Web Push requires a push event handler in the service worker, VAPID public/private key generation, a subscription endpoint stored server-side, and a push send mechanism using the Web Push Protocol. A PWA with only a caching service worker will show zero push notifications regardless of how the rest of the notification UI is built.