Love your explanation! The mirror from Shrek would definitely say thiccccc.
Leaving this here for modern contextualizing.
So fair skin doesn’t specifically mean pale, it means skin that doesn’t have defects. Bumps, pimples, scarring and other things will tarnish the complexion of skin.
In this context it’s not racial, it’s colorism as you explained it was a status thing. Something that exists in almost every culture, not just European.
That’s because it’s the brotherhood of steel of course!