What you said is about the subjective aspect. But what I'm saying is that it can be mathematically balanced, but what they are doing doesn't seem to be true.

My definition of mathematically balance would be for the palette (which is N points in the colorspace) to have a certain relationship according to the metric. One example relationship would be for them to be for all nearest neighbors sharing the same distance (which might not be possible.) The one I have in mind is for a sub-set of them forming this relationship in a potentially tilted plane, and probably have 2 such planes with a certain distance apart. The symmetry in the metric probably allows you to find 2 such planes that is equidistance with the center which can then have nicer properties about the relationships between points on opposite planes.

All these are easy if the metric is Euclidean, which is approximately true with some colorspace. It would be much more complicated if the empirical metric is taken into account.

Bottom line is I expect them to define what mathematical balanced means and there seems none.

The "mathematically balanced" description seems to be selling itself short actually. If you check the actual description, it says "By using the perceptually uniform colour space Oklab, I was able to achieve perceptually uniform hue differences between each of the accent colours, ensuring maximum differentiability between highlighted words. Constant chroma ensures none of them stand out from or recede into the page more than others."

Doing the balancing in Oklab specifically addresses your point about perception in our eyes.