Getting my player to move in the direction it is facing.

I am new to unity and I am trying to get my player to move based on transform.forward, but It still moves based on the world space, I can't get anything to work.

Heres the code:

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

 public class AnimationAndMovementController : MonoBehaviour
 {

 PlayerInput playerInput;
 CharacterController characterController;
 Animator animator;

 Vector2 currentMovementInput;
 Vector3 currentMovement;
 Vector3 currentRunMovement;
 bool isMovementPressed;
 bool isRunPressed;
 float rotationFactorPerFrame = 5.0f;
 float runMultiplier = 3.0f;
 public Transform cam;



 void Awake()
 {
     playerInput = new PlayerInput();
     characterController = GetComponent<CharacterController>();
     animator = GetComponent<Animator>();

     playerInput.CharacterControls.Move.started += onMovementInput;
     playerInput.CharacterControls.Move.canceled += onMovementInput;
     playerInput.CharacterControls.Move.performed += onMovementInput;
     playerInput.CharacterControls.Run.started += onRun;
     playerInput.CharacterControls.Run.canceled += onRun;
 }

 void onRun (InputAction.CallbackContext context)
 {
     isRunPressed = context.ReadValueAsButton();
 }

 void onMovementInput (InputAction.CallbackContext context)
 {
     currentMovementInput = context.ReadValue<Vector2>();
     currentMovement.x = currentMovementInput.x;
     currentMovement.z = currentMovementInput.y;
     currentRunMovement.x = currentMovementInput.x * runMultiplier;
     currentRunMovement.z = currentMovementInput.y * runMultiplier;
     isMovementPressed = currentMovementInput.x != 0 || currentMovementInput.y != 0;
 }

 void handleAnimation()
 {
     bool isWalking = animator.GetBool("isWalking");
     bool isRunning = animator.GetBool("isRunning");

     if (isMovementPressed && !isWalking) {
         animator.SetBool("isWalking", true);
     }

     else if (!isMovementPressed && isWalking) {
         animator.SetBool("isWalking", false);
     }

     if ((isMovementPressed && isRunPressed) && !isRunning)
     {
         animator.SetBool("isRunning", true);
     }

     else if ((!isMovementPressed || !isRunPressed) && isRunning) {
         animator.SetBool("isRunning", false);
     }
 }

 void handleGravity()
 {
     if (characterController.isGrounded) {
         float groundedGravity = -.05f;
         currentMovement.y = groundedGravity;
         currentRunMovement.y = groundedGravity;
     } else {
         float gravity = -9.8f;
         currentMovement.y += gravity * Time.deltaTime * 2.0f;
         currentRunMovement.y += gravity * Time.deltaTime * 2.0f;
     }
 }

 // Update is called once per frame
 void Update()
 {
     handleAnimation();
     handleGravity();

     if (isRunPressed) {
         characterController.Move(currentRunMovement * Time.deltaTime);
     } else {
         characterController.Move(currentMovement * Time.deltaTime);
     } 
 }

 void OnEnable()
 {
     playerInput.CharacterControls.Enable();
 }

 void OnDisable()
 {
     playerInput.CharacterControls.Disable();
 }

}