Trouble with positions of vertices

So I scripted a mesh, which looks like this:

(Yellow spheres are the vertices)(I named it "Ground")

I only need the drawn upside part of the mesh for this question

I also added a mesh collider to it and then created a new gameobject with a rigidbody attached to it.

They collide fine

I want to create a new vertex at exactly the position where they collided. So I used the OnCollisionStay() function:

 void OnCollisionStay(Collision collision)
     {
         ContactPoint contact = collision.contacts[0];
 
         if (contact.otherCollider.name == "Ground")
         {
 
             //Process of collision vertex creation
             newVertices = new Vector3[mesh.vertexCount + 1];
 
             for (int i = 0; i < mesh.vertexCount; i++)
             {
                 newVertices[i] = mesh.vertices[i];
             }
 
             //sets the position of the new vertex
             newVertices[mesh.vertexCount] = contact.point;
 
             //applies changes
             mesh.vertices = newVertices;
 
             mesh.RecalculateNormals();
             mesh.RecalculateBounds();
         } 
     }

But I can't seem to get what I did wrong

Instead of creating the vertex exactly where the collision happened, they spawn in wrong places. (See below)

My guess is, that it has to do with the local and world spaces. I already tried different ways like using the transform.TransformPoint()

and similar to convert the contact point I created to relevant coordinates, but nothing.

What did I do wrong? Can you help me?