Not sure. The article is long and I only skimmed it, but what stood out to me were the following paragraphs:

"After trying to fix Oklab for a dozen of hours, it appeared that the numerical issues it raises are grounded into design constraints we don’t need for the current task. And so do most of the other perceptual spaces.

[..]

So we could fit an Lch model directly from Munsell hue-value-chroma dataset, without going through LMS space and without even tilting the lightness plane. Doing so, we will not try to model the physiology of vision, but approach the problem as a geometric space distortion where the Munsell hues and the saturations (as a ratio of chromas / values) can be predicted by a 1D mapping from the hues, chromas and lightnesses of forming the principal dimensions of the model.

This model will need to be invertible. We will try to fit brightness data to derivate correlates of perceptual brightness accounting for the Helmholtz-Kohlrausch effect. Using the brightness and saturation correlates, we will rewrite our image saturation algorithm in terms of perceptually-even operators."

They obviously took a lot from Oklab but it seems to me they did more than just modifying it to reduce the residual error. But again, I just skimmed and I can be completly wrong.