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Is there possibly a way to render the face normals in Eevee as they are displayed in the viewport?

I have two simple shapes here as an example. These use a simple Checker texture.

enter image description here

In the viewport, I can now enable the Face Orientation option in the overlays:

enter image description here

This additionally displays the normals of the faces in red and blue mixed with the underlying texture:

enter image description here

Is there any way to reconstruct this effect with Eevee so that I essentially get in the rendered image the result that the overlay in the viewport creates for me?

Note: I'm looking for a way to solve this with a material, because this effect should not be applied to the whole scene, but only to a specific object with a specific material!

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Having encoded back and front facing with red and blue:

enter image description here

It looks as if it could be a simple Add to the original texture, as above .. but I have to confess to having trouble getting an exact match:

enter image description here

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    $\begingroup$ Thank you very much! This works perfectly for my use case, because I don't need an exact reproduction of the effect, but only an additional coloring of the materials, caused by the orientation of the faces! $\endgroup$
    – quellenform ♦
    Feb 4 at 19:54

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