unless that texture is specifically made to act like UV coordinates, sadly adjusting UV’s after a texture node is not a thing.
UV coordinates are nothing more than X and Y gradients, using vertices to map locations on those X and Y coordinates. since a texture (unless specifically a uv-texture) has a variety of gradients and hues there is no way to adjust their coordinates afterward.
the custom UV input can do more than just panning though, you can forward most math through it, albeit on a vertex level, not pixel level. And since its on vertex level, you can use each vertex channel (RGBA) for their own purposes. though vertices that contain more than one color (RGB) can cause issues.