SignUp.tsx

// ...

const SignUp: React.FC = () => {
  // ...
  
  useEffect(() => {
    firebase.auth().onAuthStateChanged(user => {
      if (user) {
        // user signed in
      } else {
        // user not signed in
      }
    })
  }, [])

  const handleSignUpWithGitHub = useCallback(async () => {
    const provider = new firebase.auth.GithubAuthProvider()

    try {
      const currentUser = await firebase.auth().currentUser

      const res = currentUser
        ? await currentUser.linkWithPopup(provider)
        : await firebase.auth().signInWithPopup(provider)

      console.log('res: ', res)
    } catch (err) {
      // error handling
      console.error(err)
    }
  }, [])

  // ...
  
  return (
    // ...
        <Grid container spacing={2}>
          <Grid item xs={12}>
            <GithubLoginButton
              className={classes.github}
              onClick={handleSignUpWithGitHub}>
              <span className={classes.githubText}>Sign up with Github</span>
            </GithubLoginButton>
          </Grid>
   // ...
  )
}

export default SignUp