Follow camera is not turning when the followed object turns

Question

I need a camera follow script to chase a moving ball. I've attached the script below to my camera, but when the ball turns left and right the camera does not turn

using UnityEngine;

public class FollowPlayerCamera : MonoBehaviour
{
    public GameObject[] playerBalls; // Array of player balls
    public float smoothSpeed = 0.125f; // How smoothly the camera follows the ball
    public Vector3 offset; // Offset from the ball position

    private ActivatePlayer playerController; // Reference to the BallPlayerController script
    private Transform target; // The current active player to follow

    void Start()
    {
        playerController = FindObjectOfType<ActivatePlayer>();
        if (playerController != null)
        {
            // Ensure there is at least one player in the array
            if (playerBalls.Length > 0)
            {
                // Set the first player in the array as the initial target
                target = playerBalls[playerController.selectedPlayerIndex].transform;
            }
        }
        else
        {
            Debug.LogWarning("BallPlayerController script not found in the scene!");
        }
    }

    void LateUpdate()
    {
        if (playerController == null)
        {
            return;
        }

        // Find the active player to follow
        if (playerController.selectedPlayerIndex >= 0 && playerController.selectedPlayerIndex < playerBalls.Length)
        {
            target = playerBalls[playerController.selectedPlayerIndex].transform;
        }

        if (target == null)
        {
            // If there's no target, exit the function
            return;
        }

        // Calculate the desired position of the camera
        Vector3 desiredPosition = target.position + offset;

        // Interpolate smoothly towards the desired position
        Vector3 smoothedPosition = Vector3.Lerp(transform.position, desiredPosition, smoothSpeed);

        // Set the camera's position
        transform.position = smoothedPosition;
    }
}