Add Physics to Character Movement

I'm not new to programming, but I'm new to Unity. I'm making a basic 2D platformer with movement defined as follows:

     void Update()
     {
         CharacterController controller = GetComponent<CharacterController>();
         float rotation = Input.GetAxis("Horizontal");
         if(controller.isGrounded)
         {
             moveDirection.Set(rotation, 0, 0); //moveDirection = new Vector3(rotation, 0, 0);
             moveDirection = transform.TransformDirection(moveDirection);
             
             //running code
             if(Input.GetKey(KeyCode.LeftShift) || Input.GetKey(KeyCode.RightShift)) //check if shift is held
             { running = true; }
             else
             { running = false; }
             
             moveDirection *= running ? runningSpeed : walkingSpeed; //set speed
             
             //jump code
             if(Input.GetButtonDown("Jump"))
             {
                 moveDirection.y = jumpHeight;
             }
         }
         moveDirection.y -= gravity * Time.deltaTime;
         controller.Move(moveDirection * Time.deltaTime);
 }

This is currently alright, but it has some flaws. For example, the jumping continues even if I hit a ceiling (so it sticks to the ceiling until the jump is complete) rather than stopping right away. So I was wondering, how can I use Unity's physics to improve this character's design?