That’s because tangent space normal maps aren’t really compatible with box projection, they depend on UV data for the orientation of their shading and you have no control over that with an automated projection.
It probably looked good before the remesh because the faces were placed differently. The remeshing just made the problem more visible because the topology is more complex and that caused a patch to take a different direction from the rest. But it’s not unlikely that even without the remesh, you would find some wonky stuff happening (like places with inverted normal map shading) if you went searching for it with a light source.
Does the set of textures you are using have a displacement/height map? Use that with a bump node instead of the normal map, that’s compatible with box mapping.