Rendering with GL.Begin to a RenderTexture does not update it continuously (2019.2)

So I am trying to render a trianglestrip to a rendertexture. For this I created a small script that takes a bunch of transforms and a rendertexture and draws a trianglestrip that connects the transforms. For simplicity, I assume the transforms are already in UVspace and use an identity matrix.

 public class GLRenderTextureTest : MonoBehaviour {
     public List<Transform> targets;
     public RenderTexture rt;
     private Material UVMaterial;
 
     void Start() {
         UVMaterial = new Material(Shader.Find("Unlit/TestShader"));
     }
     
     void Update() {
         RenderTexture.active = rt;
         UVMaterial.SetPass(0);
 
         GL.PushMatrix();
         GL.LoadIdentity();
 
         GL.Begin(GL.TRIANGLE_STRIP);
 
         for (int i = 0; i < targets.Count; i++) {
             GL.Vertex3(targets[i].position.x, targets[i].position.z, 0);
         }
 
         GL.End();
         GL.PopMatrix();
 
         RenderTexture.active = null;
     }
 }

And this is what it looks like in the scene:

But if I then go and move one of the transforms, the rendertexture does not update!

I feel like this should be working. I've already exhausted all solutions the google search results provided, to no avail. So here I am, stuck with a simple task, not knowing how to fix this.

To reproduce:

1. Create a new 3D project.

2. Create a new RenderTexture RT, no depth buffer, size 1024x1024

3. Create a new Material M

4. Add RenderTexture RT to Material M

5. Create a new Unlit Shader and name it TestShader

6. Add a quad to the scene, rotate by 90° x, scale 2, pos in zero

7. Add Material M to Quad

8. Add 8 (or any x >=3) spheres to the scene, scale 0,05f, place them inside the quad area

9. Add a new script called GLRenderTextureTest, copy code from above

10. Add spheres and rendertexture to the script in inspector

11. save scene

12. hit play and move any sphere