Rotate and Move towards Mouse Point

I am trying to apply forward movement and rotation, however I can not get the two to mix. So far, only rotation works the way it should. Forward movement, under a Character Controller .move, ignores the rotation and keeps going straight.

My code so far stands as:

 transform.LookAt(posistion);
 transform.rotation = Quaternion.Euler(new Vector3(0, transform.rotation.eulerAngles.y, 0));
                     
 Vector3 mover = new Vector3(0,0,3);
                     
 mover = mover * Time.deltaTime * 4;
                     
 controller.Move(mover);    

Posistion represents the actual mouse, and I'm rotating along the Y axis for a top-down game. The mouse controls where the player goes, although not by clicking.