Edit: You have to actually click for a full size image to see the truth. Those inline images had pretty bad compression artefacts, even the supposed lossless versions.
So https://eng.aurelienpierre.com/wp-content/uploads/sites/8/20... (full size lossless WebP image) looks fine, but inline version of the same image https://eng.aurelienpierre.com/wp-content/uploads/sites/8/20... looks terrible.
Edit 2: The difference between...
https://eng.aurelienpierre.com/wp-content/uploads/sites/8/20... lossy-noise.jpg (216 kB JPEG)
https://eng.aurelienpierre.com/wp-content/uploads/sites/8/20... (150 kB WebP)
https://eng.aurelienpierre.com/wp-content/uploads/sites/8/20... (301 kB WebP)
... is pretty obvious. Both of the WebP examples, even that 301 kB version, show clearly visible posterization.
I wonder if there's some issue with the WebP encoder (or the settings) he is using?
Edit 3:
It should be noted that monitor gamma and color profile might affect gradient posterization visibility.