adding users to firestore with the same uid that it was created with

Question

I am trying to add new users to firestore with the same uid, when they are creatd with createUserWithEmailAndPassword. however I can add users to my user collection, but the id its given is not the same id as the uid. this is how I do it:

    const auth = getAuth(db);
      const app = getFirestore();

 const handleSubmit = useCallback(
    async (event) => {
      event.preventDefault();

      const { email, password, fname, lname } = event.target.elements;
      // console.log("clicked", email.value, password.value);

      const auth = getAuth(db);
      const app = getFirestore();
      createUserWithEmailAndPassword(auth, email.value, password.value)
        .then(async (userCredential) => {
          // Signed in
          const user = userCredential.user;

          try {
            const docRef = await addDoc(collection(app, "users"), {
              firstName: fname.value,
              lastName: lname.value,
              email: email.value,
              age: 0,
              bday: "",
            });
            console.log("Document written with ID: ", docRef.id);
          } catch (e) {
            console.error("Error adding document: ", e);
          }

          //=================
        })
        .catch((error) => {
          const errorCode = error.code;
          const errorMessage = error.message;
          // ..
        });
    },
    [history]
  );

the ref id it a different id than my uid. what do I have to do to make it save the user with the same id.

also I have tried this

app.collection("users")
doc(user.uid)
.set({...})

but this generates an error!