The author doesn’t understand/communicate-well what a n-bit color palette means, which then confused the rest of us. It refers to the complete size of the palette, in 2^n of course.

She created a 12-entry indexed palette, from the 12-bit (4096) possibilities of short css-hex codes, one nibble per char. (Also single css-hex codes double, so results are brighter than expectations.)

Tldr: This is a 12-entry indexed palette, not a 12-bit one. Neither of which we are constrained to.