It seems like some work was done to research existing approaches, but I don't see any reference to Pantone Skin Tones [0]. Without intending to, I've worked on 3 different projects which involved measuring skin tones for makeup applications. The Pantone range is not 100% perfect, but it's pretty well done and easy to understand. There are two axes: a light/dark one, and red-yellow one [1].
[0] https://www.pantone.com/na/en-us/skintone
[1] https://cosmeticsbusiness.com/pantone-skintone-guide-80945