“It doesn’t work” is not enough information to work with to help you find out why. There must have been a problem and it’s in your file, or it’s a graphics problem.
Try this one. Second scene layer has another torus that fixes the minor shading/reflection issue on every other column of square indentations.
subdivision_reflections_datatransfer_ja12.blend (319 KB)
To recap, the result subdivision surfaces give you is not perfect for everything. Small details on a curved surface is an example which makes you fight against the advantages subdivision surfaces give you because those details need geometry for you to control the subdivision on them too.
More control geometry on a curved surface means adding it on the whole surface, not just where the detail is (unless you can do a loop reduction), which means smaller angles between polygons along the surface and less need for subdivision. And even when you do that it might not be satisfactory enough for some purposes, like having uniform reflections on a surface that subdivision makes uneven.
I added data transfer modifier to use custom normals and fix the issues on a high polygon model. Might not want to use that for a car body but fixing a perforated chrome detail for a close up shot should be fast and easy enough.
Normal map is a difference of the directions two surfaces point at. Or in other words, information that is needed to make the surface it’s on to look like it has details from another surface. Bake one surface on itself and there is no difference. Two parallel surfaces, no difference. When surface direction change along the normal of the original surface point, then there is a difference and bake result would give something else than the default values on a pixel.
Could use it to change the appearance of the surface on high polygon object but usually done to fake detail on a much lower polygon one, baked from object to the other. If there is an issue in the high polygon object, custom normals is again an option to fix the issue and then bake.
It’s data, not color, so you can’t take any paint tool and just paint on a normal map image. No one is stopping you but really shouldn’t try to fix a detail on a normal map like that because the brush has no idea of the two surfaces, it just mixes RGB values in the brush with the ones on the image.