NuxtJS Firebase V9 modular in service worker

Question

Firebase documentation says to use this code inside service worker:

import { initializeApp } from 'firebase/app'
import { getMessaging } from 'firebase/messaging/sw'

But I get this error:

Token error: FirebaseError: Messaging: We are unable to register the default service worker.

I assume that this is because WebPack under NuxtJS configuration ignores "import" inside service worker files.

Is there any way to fix this?