Sprites shake when the camera moves

Unity Engine
1

Hello, when the camera moves, the sprites of my objects shake:

If I use this code inside my camera, which should help to get the pixel perfect, the shakes stop.

    public static float RoundToNearestPixel(float unityUnits, Camera viewingCamera)
    {
        float valueInPixels = (Screen.height / (viewingCamera.orthographicSize * 2)) * unityUnits;
        valueInPixels = Mathf.Round(valueInPixels);
        float adjustedUnityUnits = valueInPixels / (Screen.height / (viewingCamera.orthographicSize * 2));
        return adjustedUnityUnits;
    }

    void LateUpdate()
    {
        Vector3 newPos = transform.position;
        Vector3 roundPos = new Vector3(RoundToNearestPixel(newPos.x, _mainCamera), RoundToNearestPixel(newPos.y, _mainCamera), newPos.z);
        transform.position = roundPos;
    }

The problem is that if I turn VSync off, the camera stutters and stop to work properly (only with the stand alond version):
VSync On:

VSync Off:

Anyone can help me pls?

This is the rest of the code of the camera:

using UnityEngine;
using System.Collections;

public class CameraController : MonoBehaviour
{
    private Transform _player;
    private Camera _mainCamera;
    private OptionsManager _optionsManager;

    private Vector2 _mousePos;
    private Vector2 _playerPos;
    private Vector2 _newPos;
    private float _dist;
    private float _maxDist = 4f;
    float x, y;
   
    public Vector2 smoothing = new Vector2(5f, 5f);

    [HideInInspector]
    public bool isCameraLocked;


    void Start()
    {
        _mainCamera = GetComponent<Camera>();
       
        _optionsManager = GameObject.FindGameObjectWithTag("MainMenuManager").GetComponent<OptionsManager>();
        UpdateOrthographicSize(_optionsManager.cameraScale);
       
         _player = GameObject.FindGameObjectWithTag("Player").GetComponent<Transform>();
        if (_player != null)
            transform.position = new Vector3(_player.position.x, _player.position.y, transform.position.z);
    }
   
    void Update()
    {
        if (isCameraLocked == false)
        {
             _mousePos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
            _playerPos = new Vector2(_player.position.x, _player.position.y);
            _newPos = _playerPos + ((_mousePos - _playerPos) / 2);
           
            x = Mathf.Lerp(transform.position.x, _newPos.x, smoothing.x * Time.deltaTime);
            y = Mathf.Lerp(transform.position.y, _newPos.y, smoothing.y * Time.deltaTime);
            transform.position = new Vector3(x, y, transform.position.z);
        }
    }

    public void UpdateOrthographicSize(int scaleIndex)
    {
        // OrthographicSize = Screen resolution height / PPU * Scale (32x8 o 32x4);
        float screenHeight = Screen.height;
        int scale;
        if (scaleIndex == 0)
            scale = 4;
        else
            scale = 8;
        _mainCamera.orthographicSize = screenHeight / (32 * scale);
    }

    public static float RoundToNearestPixel(float unityUnits, Camera viewingCamera)
    {
        float valueInPixels = (Screen.height / (viewingCamera.orthographicSize * 2)) * unityUnits;
        valueInPixels = Mathf.Round(valueInPixels);
        float adjustedUnityUnits = valueInPixels / (Screen.height / (viewingCamera.orthographicSize * 2));
        return adjustedUnityUnits;
    }

    void LateUpdate()
    {
        Vector3 newPos = transform.position;
        Vector3 roundPos = new Vector3(RoundToNearestPixel(newPos.x, _mainCamera), RoundToNearestPixel(newPos.y, _mainCamera), newPos.z);
        transform.position = roundPos;
    }

    public void UpdatePlayer(Transform playerTransform)
    {
        _player = playerTransform;
        transform.position = new Vector3(_player.position.x, _player.position.y, transform.position.z);
    }

    public void UpdatePlayer()
    {
        _player = GameObject.FindGameObjectWithTag("Player").GetComponent<Transform>();
        transform.position = new Vector3(_player.position.x, _player.position.y, transform.position.z);
    }
}

I have also a question about the refresh rate of the monitors please.
I have an Asus monitor which could run at 144Hz, but Unity doesn’t show these resolution when I use Screen.resolutions, it shows few 60Hz, many 59Hz and one at 75Hz. Why is that?

Thanks a lot.

2

The shake is due to Unity stretching the sprites and the code which I use on the camera fixes that, by rounding the position of the camera.

As I wrote, if I use that code and turn VSync off, the camera stop behaving correctly…so I tried to limit the number of FPS using “Application.targetFrameRate = 60” while VSync is off and everything works fine again.

Should I leave it like that?
Should I limit the FPS while VSync is on too? Is it automatic right?
Also should I limit the refresh rate of the monitor to 60 as well when I apply the resolution?

Thanks a lot.