I don't think that that is the case. Re-baking with the whole mesh smooth-shaded without custom normals and sharp edges will still show the issue in Eevee (but not in Cycles), although of course the normals in general would be wrong.
E.g., with Auto-Smooth disabled one can still use the 'ObjectNM' material. Eevee will preview it without banding. But, baking tangent space normals with that material, switching back to the 'TangentNM' material and plugging the new texture instead of the original TS normal map will bring back banding in Eevee (but not Cycles). Even a few seams along triangulation edges would show in Eevee (on the flat sides).

Let’s move it to bug for now… @Clément Foucault (fclem) and/or @Jeroen Bakker (jbakker) shall know more here?

It's really strange. My first guess was that it was related to the 10bit normals precision issue (T61024). But even when testing with D6614 it did not fix the problem entierly.

Then I remember that we only use 16bits texture for the GPU.

This one liner fixes is:

@@ -1060,11 +1060,11 @@ void GPU_create_gl_tex(uint *bind,
 
   /* create image */
   glGenTextures(1, (GLuint *)bind);
   glBindTexture(textarget, *bind);
 
-  GLenum internal_format = (frect) ? GL_RGBA16F : (use_srgb) ? GL_SRGB8_ALPHA8 : GL_RGBA8;
+  GLenum internal_format = (frect) ? GL_RGBA32F : (use_srgb) ? GL_SRGB8_ALPHA8 : GL_RGBA8;
 
   if (textarget == GL_TEXTURE_2D) {
     if (frect) {
       glTexImage2D(GL_TEXTURE_2D, 0, internal_format, rectw, recth, 0, GL_RGBA, GL_FLOAT, frect);
     }

However, this has some big performance impact. So I think this is an option we need to add in the future "Performance/Quality" panel for EEVEE/workbench.

Thanks for clarification. So it's not a bug per se? I wonder if that could be made an option for the texture node itself, to allow for selective sacrifices of performance to quality.

We could add a per image datablock option. We can debate what is the best option UX wise. @Brecht Van Lommel (brecht) @William Reynish (billreynish) any input on this?

I'm fine with an option on the image datablock.