update: i have added the entire file

I have uploaded an image to firebase storage, i then want to send the url to firebase realtime database under a node for a particular user.

I am using this code to try it, but i get an error saying

Cannot read properties of undefined (reading 'path')

here is the block of code I am using

The error points to this line ` set(ref(db,'users/'+auth.currentUser.uid+'/images/'+url))

import { getAuth } from "firebase/auth";
import React, { useState } from "react";
import { db } from "./util/firebase";
import { getDownloadURL, ref, uploadBytesResumable } from "firebase/storage";
import {storage} from './util/firebase'
import { set } from "firebase/database";
import {v4 as uuidv4} from 'uuid'

function AddPicture() {
  //const [image, setImage] = useState("");

  const auth = getAuth();
  const user = auth.currentUser;
  const metadata = {
      customMetadata:{
          'imageID': uuidv4(),
          'User': auth.currentUser.email,
      }
  }
 

  const uploadPicture = (e) => {
    e.preventDefault();

    const image = e.target[0].files[0];
    const imageRef = ref(storage,'/images/'+user.uid+'/'+image.name)
    

    const uploadTask = uploadBytesResumable(imageRef, image,metadata);


    if (image) {
        uploadTask.on("state_changed",
        (snapshot) => {
          console.log("Uploaded image");
          console.log('current uid'+auth.currentUser.uid)

          
        },
        (error) => 
          console.log('didnt upload '+error),
        ()=>{
            getDownloadURL(uploadTask.snapshot.ref)
            .then((url)=>{

                set(ref(db,'users/'+auth.currentUser.uid+'/images/'),url);
                console.log(url)
            })

        }
        
        )
    }
    else {
        console.log('Please Choose an image');
        alert('image type not supported');
        return;
    }
  };

  return (
    <div className="container">
      <form onSubmit={uploadPicture}>
        <input type="file" />
        <button >Upload</button>
      </form>
    </div>
  );
}

export default AddPicture;