Earlier quoted context omitted.
They want their awful webp format to win for some reason.
From a technical perspective, what are the differences between the two?
The WebP lossless format (internally "VP8L") is the second codec supported by libwebp but otherwise independent. This format can be thought as an optimized PNG; it uses the main PNG algorithm but then tweaks various bits for better compression. For this reason it is very rare to see PNG files smaller than losslessly compressed WebP files when efficiently done.
JPEG XL is very different from both. There are some technical resemblances, as the author of lossless WebP also worked on JPEG XL (and Brotli), but the overall architecture is completely revamped. The lossy portion of JPEG XL is a (much larger) superset of JPEG 1, while the lossless portion is based on a learnable context modelling respresented as a binary decision tree. And then everything got sandwiched between yet another set of components.