Unwanted up/down (pitch) movement when tilting

Hey All,

since a few days i try to solve a problem but i do not get it. Solved already parts of it but there is one problem remaining. The aim is to move the character per Input.GetAxis Horizontal & Vertical in every direction like in a topdown zelda game. When moving left the character tilts also left, same for right movement. Its already tilting always in the right direction even when flying a circle. Everything works so far the only problem is that i also get an unwanted pitch and the character flys then up and down. But i want to just have a simple movement in all directions and a local tilt on the character without unwanted pitching. I just dont get it how to calculate and fix the unwanted pitch.

Here is my actual code:

 public class MovementController : MonoBehaviour
 {
     private void Start()
     {
         forward = Camera.main.transform.forward;
         forward.y = 0;
         forward = Vector3.Normalize(forward);
         right = Quaternion.Euler(new Vector3(0, 90, 0)) * forward;
         facingDirection = transform.rotation;
     }
   
     private void GetMovementDirection()
     {
         horizontalDirection = right * Input.GetAxis("Horizontal"); //up - down
         verticalDirection = forward * Input.GetAxis("Vertical"); // left - right
         movingDirection = Vector3.Normalize(horizontalDirection + verticalDirection);
  
         rotationSpeed = Sensitivity * (Mathf.Clamp01(new Vector2(Input.GetAxis("Horizontal"), Input.GetAxis("Vertical")).sqrMagnitude));
     }
  
     private void MoveCharacter()
     {
         //rigidbodyPlayer.MovePosition(rigidbodyPlayer.position + transform.forward * Time.deltaTime * movementSpeed);
         rigidbodyPlayer.MovePosition(rigidbodyPlayer.position + movingDirection * Time.fixedDeltaTime);
     
         if (movingDirection != Vector3.zero)
         {
             facingDirection = Quaternion.LookRotation(movingDirection, Vector3.up);
         }
         transform.rotation = Quaternion.Slerp(transform.rotation, facingDirection, Time.deltaTime * rotationSpeed);
     }
  
     private void TiltCharacter()
     {
         if (turnLeft)
         {
             targetRotation = Quaternion.AngleAxis(60f, transform.forward) * transform.localRotation;
             transform.localRotation = Quaternion.RotateTowards(transform.localRotation, targetRotation, leftIntensity * 3.0f);
         }
         else if (turnRight)
         {
         //same for right movement
         }
         else
         {
          // reset position
         }
     }
 }

Maybe someone can push me in the right direction. Thanks in Advance!