How to make camera follow a rolling ball from behind it in Unity?

So I need help making a script where the camera follows a rolling ball (controlled by the player) always from behind it, so if it rotates right, the camera will too but still remain behind the ball facing in the direction the ball is moving and without exactly rotating around the x and z axis.

Its been a month since I've started programming and this is the best I could do however it's very janky, doesn't flow nicely and isn't exactly what I want:

void Start()
{
    offset = transform.position - player.transform.position;
}

// Update is called once per frame
void LateUpdate()
{
    CameraMovement();
    
}

private void CameraMovement()
{
    float inputX = Input.GetAxis("Horizontal");
    float inputZ = Input.GetAxis("Vertical");

    if (inputX > 0)
    {
        transform.position = player.transform.position + new Vector3(-3.5f, 2f, 0f);
        transform.LookAt(player.position);
    }
    else if (inputX < 0)
    {
        transform.position = player.transform.position + new Vector3(3.5f, 2f, 0f);
        transform.LookAt(player.position);
    }

    if(inputZ > 0)
    {
        transform.position = player.transform.position + new Vector3(0f, 2f, -3.5f);
        transform.LookAt(player.position);
    } else if(inputZ < 0)
    {
        transform.position = player.transform.position + new Vector3(0f, 2f, 3.5f);
        transform.LookAt(player.position);
    }
    else if(inputX == 0 && inputZ == 0)
    {
        transform.position = player.transform.position + new Vector3(0f, 5f, 0f);
        transform.LookAt(player.position);
    }
}`   

As mentioned I would decouple this from the input and rather handle the balls movement and do something like e.g.

public class CameraController : MonoBehaviour
{
    public Transform player;

    private Vector3 offset;
    private Vector3 previousPosition;
    private Quaternion targetRotation;
    private Vector3 targetPosition;
    private Vector3 currentVelocity;
    private float currentRotVel;

    // Start is called before the first frame update
    private void Start()
    {
        previousPosition = player.position;
        offset = transform.position - previousPosition;

        targetRotation = transform.rotation;
        targetPosition = transform.position;
    }

    // Update is called once per frame
    private void LateUpdate()
    {
        var position = player.position;
        // direction is simply the delta between last and this frame positions
        var direction = position - previousPosition;
        previousPosition = position;

        if (direction != Vector3.zero)
        {
            // look in move direction
            targetRotation = Quaternion.LookRotation(direction);
            // apply offset in move direction
            targetPosition = position + targetRotation * offset;
        }

        // [optional] smoothly move into position and rotation
        transform.rotation = QuaternionUtils.SmoothDamp(transform.rotation, targetRotation, ref currentRotVel, 0.5f);
        transform.position = Vector3.SmoothDamp(transform.position, targetPosition, ref currentVelocity, 0.5f);
    }
}

// little helper for a SmoothDamp equivalent for Quaternion
public static class QuaternionUtils
{
    public static Quaternion SmoothDamp(Quaternion from, Quaternion to, ref float currentAngularVelocity, float smoothTime)
    {
        var delta = Quaternion.Angle(from, to);
        if (delta > 0f)
        {
            var t = Mathf.SmoothDampAngle(delta, 0.0f, ref currentAngularVelocity, smoothTime);
            t = 1.0f - t / delta;
            return Quaternion.Slerp(from, to, t);
        }

        return to;
    }
}

depends on your use case of cause, you can of course as well keep applying the input directly and get the direction that way instead basically mirroring the way you use and apply the user input to the player movement e.g.

var direction = player.transform.right * Input.GetAxis("Horizontal") + player.transform.forward * Input.GetAxis("Vertical");

Look, this can be done much easier than it is now. You can move the input reading logic into a separate component (for example, PlayerInput), and then a script, for example, CharacterMovement, will work with this input. In the CameraMovement component, you can simply take the player's position, add a certain offset to it, and set the resulting coordinate as the camera's position. Сamera rotation set to player rotation. The code will look something like this:

[SerializeField] private Transform _playerTransform;
[SerializeField] private Vector3 _offset;
    
private void LateUpdate()
{
    transform.position = _playerTransform.position + _offset;
    transform.rotation = _playerTransform.rotation;
}