So you’re looking to add noise to a texcoord to simulate a noisy blurring of a texture? If you want it to “blur” evenly in all directions, you can only guarantee the blur is even in UV space. If you’re applying this in an object’s material, there’s no way to have screen, or even world space consistent blurs since there’s no way to know what color is in a texcoord at a specific screen or world position outside of the triangle currently being rendered. The best you can get is it to be an even blur across the model by being careful with your UV mapping to try to keep the UVs as consistent as possible, but you’ll get artifacts anywhere there’s a UV seam as there’s no way to detect those in the shader.
If this is a screen space effect, then you just need to scale one axis of the texcoord offset by the screen’s aspect ratio.