I'm attempting to implement Firebase Cloud Messaging for the web using their v9 SDK, which is heavily pushing using Javascript modules... and I need to register the service worker inside of a Vue component.

The service worker keeps screaming "you cannot use import statements outside of a module". So, I tried adding the {type: 'module'} option to the navigator.serviceWorker.register call... but no luck. I also tried the old-school importScripts to no avail. The small number of examples online show <script type='module'> but that makes no sense inside of a Vue component, at least from what I understand.

Here's the entirety of the service worker:

import { fbConfig } from "/js/firebase/firebase-config.js";
import { initializeApp } from "https://www.gstatic.com/firebasejs/9.0.2/firebase-app.js"
import { getMessaging, onBackgroundMessage } from "https://www.gstatic.com/firebasejs/9.0.2/firebase-messaging-sw.js"

// Create the instance of Firebase & Messaging
const fbApp = initializeApp(fbConfig)
const messaging = getMessaging(fbApp);

onBackgroundMessage(messaging, (payload) => {
    console.log('[firebase-messaging-sw.js] Received background message ', payload);

    const notificationTitle = payload.message.notification.title;
    const notificationOptions = payload.message.notification.body;

    let outcome = self.registration.showNotification(
        notificationTitle,
        notificationOptions
    );
    console.log('[firebase-messaging-sw.js] showNotification outcome', outcome)
});

Here's where I'm attempting to register it, which is inside of the "mounted()" section of my Vue component:

        if ('serviceWorker' in navigator) {
            navigator.serviceWorker.register(
                '/firebase-messaging-sw.js', {
                    type: 'module'
                })
                .then(reg => {
                    console.log(`Service Worker Registration (Scope: ${reg.scope})`);
                })
                .catch(error => {
                    const msg = `Service Worker Error (${error})`;
                    console.error(msg);
                });
        } else {
            // happens when the app isn't served over HTTPS or if the browser doesn't support service workers
            console.warn('Service Worker not available');
        }

Any help would be appreciated.