Simple Character Controller using in Unity Engine with new Input System.

SimpleCharacterController.cs

using UnityEngine;
using UnityEngine.InputSystem;

namespace Prototype
{
    [RequireComponent(typeof(CharacterController))]
    public sealed class SimpleCharacterController : MonoBehaviour
    {
        [SerializeField]
        private CharacterController m_characterController = default;
        [SerializeField]
        private Transform m_characterTransform = default;
        [SerializeField]
        private Transform m_headTransform = default;
        [SerializeField]
        private float m_speedLookHorizontal = 0.0f;
        [SerializeField]
        private float m_speedLookVertical = 0.0f;
        [SerializeField]
        private float m_speedMovement = 0.0f;

        [SerializeField]
        private InputAction m_inputLook = default;
        [SerializeField]
        private InputAction m_inputMovement = default;

        private float m_lookAxisVertical;
        private Vector3 m_motion;

        private void Start()
        {
            UpdateHeadPosition();
        }

        private void OnEnable()
        {
            m_inputLook.Enable();
            m_inputMovement.Enable();
        }

        private void OnDisable()
        {
            m_inputLook.Disable();
            m_inputMovement.Disable();
        }

        private void Update()
        {
            Vector2 controlAxis = m_inputMovement.ReadValue<Vector2>() * m_speedMovement;
            m_motion = m_characterTransform.rotation * new Vector3(controlAxis.x, 0, controlAxis.y);
            Vector2 lookAxis = m_inputLook.ReadValue<Vector2>();
            m_characterTransform.rotation *= Quaternion.Euler(0, lookAxis.x * m_speedLookHorizontal, 0);
            m_lookAxisVertical = Mathf.Clamp(m_lookAxisVertical - lookAxis.y * m_speedLookVertical, -90.0f, 90.0f);
            m_headTransform.localRotation = Quaternion.Euler(m_lookAxisVertical, 0, 0);
        }

        private void FixedUpdate()
        {
            if (m_motion.magnitude > 0)
            {
                m_characterController.Move(m_motion * Time.fixedDeltaTime);
            }
        }

        private void UpdateHeadPosition()
        {
            m_headTransform.localPosition = new Vector3(0, m_characterController.height - m_characterController.radius, 0);
        }

#if UNITY_EDITOR
        private void Reset()
        {
            if (m_characterController == null)
                m_characterController = GetComponent<CharacterController>();
        }

        private void OnValidate()
        {
            if (m_speedMovement < 0.0f)
                m_speedMovement = 0.0f;
            if (m_headTransform != null && m_characterTransform != null)
                UpdateHeadPosition();
        }
#endif
    }
}