How to serve offline.html when no internet connection available?

Question

I'm using workbox and vuejs and I want to serve public/offline.html page when I have no internet connection.

I edit pwa section to vue.config.js for handle service-worker myself:

  pwa: {
    name: 'myapp',
    workboxPluginMode: 'InjectManifest',
    workboxOptions: {
      swSrc: path.resolve(__dirname, 'src/pwa/service-worker.js')
    }
  },

I add this code for supporting serve offline page in service-worker.js:

console.log('in pwa');

self.addEventListener('message', (event) => {
  if (event.data && event.data.type === 'SKIP_WAITING') {
    self.skipWaiting();
  }
});

// The precaching code provided by Workbox. You don't need to change this part.
self.__precacheManifest = [].concat(self.__precacheManifest || []);
// workbox.precaching.suppressWarnings()
workbox.precaching.precacheAndRoute(self.__precacheManifest, {});

self.addEventListener("fetch", function(event) {
  event.respondWith(
      fetch(event.request).catch(function() {
          return caches.match(event.request).then(function(response) {
              if (response) {
                  return response;
              } else if (event.request.headers.get("accept").includes("text/html")) {
                  return caches.match(workbox.precaching.getCacheKeyForURL('/offline.html'));
              }
          });
      })
  );
});

So when I access to www.myapp.com/en or www.myapp.com/en/about I get the offline page.

But the problem is when I access to www.myapp.com - the workbox is serve the index.html file from the cache.

I can remove index.html from the cache, but when I online I DO WANT to serve the index from tehe cache.

So I am here in dilemma, how to do that?