Rotate (facing mouse position) a Line Renderer used as Bezier curve

Hey there I am trying to rotate a Bezier curve following the mouse position, but the curve needs to stay at its current radius.

This is my Bezier Curve code :

 public class BezierCurve : MonoBehaviour
 {
     public Vector3 p0;
     public Vector3 p1;
     public Vector3 p2;
 
     public LineRenderer lineRenderer;
     [Range(1, 64)]
     public int vertexCount = 12;
 
     private void Update()
     {
         List<Vector3> pointList = new List<Vector3>();
         for (float ratio = 0f / vertexCount; ratio <= 1; ratio += 1.0f / vertexCount)
         {
             Vector3 tangentLineVertex1 = Vector3.Lerp(p0, p1, ratio);
             Vector3 tangentLineVertex2 = Vector3.Lerp(p1, p2, ratio);
             Vector3 bezierPoint = Vector3.Lerp(tangentLineVertex1, tangentLineVertex2, ratio);
             pointList.Add(bezierPoint);
         }
         lineRenderer.positionCount = pointList.Count;
         lineRenderer.SetPositions(pointList.ToArray());
     }
 
     private void OnDrawGizmos()
     {
         Gizmos.color = Color.green;
         Gizmos.DrawLine(p0, p1);
         Gizmos.color = Color.cyan;
         Gizmos.DrawLine(p1, p2);
 
         Gizmos.color = Color.red;
         for (float ratio = 0.5f / vertexCount; ratio < 1; ratio += 1.0f / vertexCount)
         {
             Gizmos.DrawLine(Vector3.Lerp(p0, p1, ratio),
                 Vector3.Lerp(p1, p2, ratio));
         }
     }
 }

I tried this method on each of my point and the rotation is correct but spin in an non controllable way :

         Vector2 b = Camera.main.WorldToViewportPoint(p0);
         Vector2 a = (Vector2)Camera.main.ScreenToViewportPoint(Input.mousePosition);
         float angle = Mathf.Atan2(a.y - b.y, a.x - b.x) * Mathf.Rad2Deg;
         p0 = Quaternion.Euler(new Vector3(0f, 0f, angle)) * p0;
         p1 = Quaternion.Euler(new Vector3(0f, 0f, angle)) * p1;
         p2 = Quaternion.Euler(new Vector3(0f, 0f, angle)) * p2;

I am not exactly sure how I can just apply a rotation to all my point where`p1` should be pointing to the mouse position to ensure that the curve is properly align with my mouse.

Here a small screen shot of how it looks right now :