USE HIGHLIGHTS RECONSTRUCTION. Signal is damaged, green clipped first, luminance is destroyed and inconsistent with neighbourhood, it needs reconstruction, aka interpolation of the texture in 2D. Saturation, tone-mapping and such are 1D. You will not patch a 2D hole with a 1D method.
If reconstructing highlights was as simple as desaturating, I wouldn’t have spent 2 months on guided laplacian.
Saturation doesn’t care about luminance and doesn’t care about norm. Desaturating keeps luminance and hue unchanged, and degrade color to the grey having the same luminance. The norm is used here to decide if there is desaturation or not, as kind of mask, but ultimately the desaturation does not use it.