index.mjs

import { GoogleAuthProvider, initializeAuth } from "firebase/auth";

chrome.identity.getAuthToken({ 'interactive': true }, async (token) => {
    const credential = GoogleAuthProvider.credential(null, token);
      try {
        const app = initializeApp({/** Your app config */});
        const auth = initializeAuth(app, {popupRedirectResolver: undefined});
        const {user} = await auth.signInWithCredential(credential)
        console.log(`the user object is here! - ${user}`)
      } catch (e) {
        console.error(error);
      }
}); 

package.json

{
  "name": "firebase-auth-remote-code-demo",
  "version": "1.0.0",
  "description": "",
  "main": "index.js",
  "type": "module",
  "scripts": {
    "test": "echo \"Error: no test specified\" && exit 1",
    "build": "rollup -c rollup.config.js"
  },
  "keywords": [],
  "author": "",
  "license": "ISC",
  "dependencies": {
    "firebase": "9.18.0"
  },
  "devDependencies": {
    "@rollup/plugin-node-resolve": "^15.2.1",
    "rollup": "^3.29.3"
  }
}

rollup.config.js

import { nodeResolve } from '@rollup/plugin-node-resolve';

export default {
  input: './index.mjs',
  output: {
    file: './bundle.js',
    format: 'iife'
  },
  plugins: [nodeResolve()]
};