Normal map Render looks different in Cycles and Eevee

This is what I see in Eevee which is what I want:

But this is what I get in Cycles:

Any idea what is going on?
Blend file:

Would you repost the link with the images packed into the blend file? I tried looking at it, but the normal maps aren’t included

Sorry I’m not that familiar with Blender yet. I’ve done the File ‣ External Data ‣ Pack All Into .blend. Let me know if that works.