FakeBroomPhysics.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class FakeBroomPhysics : MonoBehaviour
{
    [SerializeField]
    // Assign the Transform that contains the broom head model
    Transform broomHead = default;

    [SerializeField]
    // Smooths out the rotation to reduce jitter
    float smoothing = 8f;

    private Vector3 lastPosition = Vector3.zero;
    
    // This works fine but you may want to re-write this to remove Y-axis value, so it will only track X-axis and Z-axis movement
    private Vector3 velocity { get { return broomHead != null ? lastPosition - broomHead.transform.position : Vector3.zero; } }

    private void Update()
    {
        if (broomHead == null) { return; }

        if (velocity != Vector3.zero)
            broomHead.transform.rotation = Quaternion.Slerp(broomHead.transform.rotation, Quaternion.LookRotation(-velocity), Time.deltaTime * smoothing);

        lastPosition = broomHead.transform.position;
    }
}