You’re outputting the local space normals of the object. Unity uses a left handed coordinate system for local and world space, but OpenGL tangent space normal maps are right handed. To explain that in a more straightforward way, the local Z (blue color) is pointing away from the camera in your shader, but points towards the camera in a normal map.
However it should be noted this isn’t really correct either, as depending on your camera orientation the resulting normals may not be facing the correct orientation for tangent space normals. For example, it looks like your camera is facing slightly downward, and that’s going to translate into the tangent space normal map’s normals also being rotated like that which you likely do not want.
So the more correct solution is to transform the object space normals into view space, like this: