Probleme Firebase Database

[PrimoCenturio]

Hallo zusammen,

ich bin neu in der JS Programmierung und ich hoffe hier noch einiges zu lernen.

Hier habe ich mein erstes Problem wo ich eure Hilfe bräuchte. Hier der Code

Code:

  // Import the functions you need from the SDKs you need
  import { initializeApp } from "https://www.gstatic.com/firebasejs/10.11.0/firebase-app.js";
  import { getAuth, createUserWithEmailAndPassword } from "https://www.gstatic.com/firebasejs/10.11.0/firebase-auth.js";
  import { getDatabase, ref, set } from "https://www.gstatic.com/firebasejs/10.11.0/firebase-database.js";

  // TODO: Add SDKs for Firebase products that you want to use
  // https://firebase.google.com/docs/web/setup#available-libraries
  // Your web app's Firebase configuration
  const firebaseConfig = {
    apiKey: "XXXXXXXXXXXXXXXXXXXX,
    authDomain: "XXXXXXXXXXXXXXXXXXXX",
    projectId: "XXXXXXXXXXXXXXXXXXXX",
    storageBucket: "XXXXXXXXXXXXXXXXXXXX",
    messagingSenderId: "XXXXXXXXXXXXXXXXXXXX",
    appId: "XXXXXXXXXXXXXXXXXXXX"
  };
  // Initialize Firebase
  const app = initializeApp(firebaseConfig);
  //submit button
  const registration = document.getElementById('registration');
  registration.addEventListener("click", function (event) {
    event.preventDefault();

  //inputs
  const email = document.getElementById('email').value;
  const password = document.getElementById('password').value;
  const name = document.getElementById('name');
  const prename = document.getElementById('prename');
  function AddData(){
    const db =getDatabase();
    set(ref(db, 'user/' + name), {
        name: name.value,
        prename: prename.value,
    })
    .then(()=>{
      alert("Daten wurden erfolgreich übermittelt");
    })
    .catch((error)=>{
      alert("Unsuccssful")
    })
  }
  const auth = getAuth();
 
  createUserWithEmailAndPassword(auth, email, password)
    .then((userCredential) => {
      // Signed up
      const user = userCredential.user;
      alert("Benutzer wurde erstellt")
      // ...
    })
    .catch((error) => {
      const errorCode = error.code;
      const errorMessage = error.message;
      alert(errorMessage)
      // ..
    });
  })

Die Authentifizierung funktioniert, jedoch nicht das eintragen der Daten auf Firebase Database. Sieht jemand evtl was ich falsch mache?

Danke euch vorab.

Viele Grüsse

Primo