Cinematic feel for 3D First Person Camera

Hi you guys :)

Im a grap$$anonymous$$c designer working on some virtual first person online gallery where you can walk trough and look at 3D objects. Altough i like games, i want the camera movement to be more cinematic and smooth, rather than beeing "gamy" (strictly following the mouse cursor).

There should be some z-offset like in in 2D Games, where the camere moves a bit further before following the cursor again so the whole movement feels like a camera dolly ride. I hope you get what i mean :)

So down there is my script. Im no coding pro, so really looking forward to help from you guys :)

All the best, Luis

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class PlayerLook : MonoBehaviour
 {
     [SerializeField] private string mouseXInputName, mouseYInputName;
     [SerializeField] private float mouseSensitivity;
     [SerializeField] private Transform playerBody;
     private float xAxisClamp;
     private void Awake()
     {
         LockCursor();
         xAxisClamp = 0.0f;
     }
     private void LockCursor()
     {
         Cursor.lockState = CursorLockMode.Locked;
     }
     private void Update()
     {
         CameraRotation();
     }
     private void CameraRotation()
     {
         float mouseX = Input.GetAxis(mouseXInputName) * mouseSensitivity * Time.deltaTime;
         float mouseY = Input.GetAxis(mouseYInputName) * mouseSensitivity * Time.deltaTime;
         xAxisClamp += mouseY;
         if(xAxisClamp > 90.0f)
         {
             xAxisClamp = 90.0f;
             mouseY = 0.0f;
             ClampXAxisRotationToValue(270.0f);
         }
         else if (xAxisClamp < -90.0f)
         {
             xAxisClamp = -90.0f;
             mouseY = 0.0f;
             ClampXAxisRotationToValue(90.0f);
         }
         transform.Rotate(Vector3.left * mouseY);
         playerBody.Rotate(Vector3.up * mouseX);
     }
     private void ClampXAxisRotationToValue(float value)
     {
         Vector3 eulerRotation = transform.eulerAngles;
         eulerRotation.x = value;
         transform.eulerAngles = eulerRotation;
     }
 }