background.js

chrome.runtime.onInstalled.addListener(() => {
  await syncUser()
  const {tokens, isSignedIn} = chrome.storage.sync.get('authentication')
  // initiate signup flow on my web app if user isn't signed in yet
  if (!isSignedIn && !tokens) {
    chrome.tabs.create({url : "proprietary.web.app/signup"})
  }
}) 

chrome.runtime.onMessage.addListener((message) => {
  // Gmail page oened, sync `user`
  if (message === 'open-extension') {
    await syncUser();
  }
})

chrome.runtime.onMessage.addListener(async (message, data) => {
  if (message === 'create-event') {
    const { tokens } = data
    // backend sets httpOnly cookie with token
    const res = await fetch('proprietary.web.app/api/token', { headers: {Authorization: `Bearer ${tokens.refreshToken}`} })
    
    // use token to make actual request
    const data = fetch('proprietary.web.app/api/events', {method: "POST", headers: { Authorization: `Bearer ${token}`}})
    
    // invalidate storage
    chrome.storage.sync.set({ events: data })
    return data
  }
})

const syncUser = async () => {
  // see if we can find a cookie that has been set in our backend
  const { tokens, isSignedIn } = chrome.cookies.get(
    {name: "authentication", url: "proprietary.web.app"}
  )

  if (isSignedIn && tokens) {
    // the content page will refer to `storage` to obtain authentication status
    await chrome.storage.sync.set({authentication: {tokens, isSignedIn}})
    console.log('user is signed in');
  });
  else {
    await chrome.storage.sync.set({authentication: {isSignedIn: false}})
    console.log('user has to sign in')
  }
}

content.js

// button shows only if isSignedIn === true
// const {tokens, isSignedIn} = chrome.storage.sync.get('authentication')

function Button() {
  return (
    <button onClick={() => {
        const res = chrome.runtime.sendMessage('create-event')
        initializeSomething(res);
      });
    }}>Create event</button>
  )
}

signup.jsx

function SignupPage() {
  return (
    <div>
      <button onClick={() => fetch('proprietary.web.app/signup', {method: 'POST'})}>Sign in with Google</button>
    </div>
  )
}