Both. The members use 12 bit depth.

These look fantastic as demoed here: https://grid.iamkate.com

Each of the 8-bit channels is only allowed 16 different values, i.e. needs 4 bits to represent. I think it's reasonable to describe three 4-bit channels as 12-bit colour?

Both: the resulting colors are specified as 4-bit component values, one for each of R, G, and B

Right. The very same palette can be done with usual 24- and 32- bit palette. A palette is supposed to be a (chosen) subset of the whole color space. So this is a 12 colors palette over a (presumably) 24hbit color space. A 12-bit palette should have 4096 different colors to be enumerated.

That one is a 4-bit palette.

12 bit is 4096 colors. This is 12 colors, or 3.585 bits (Usually rounded up to 4 bits to make 16 colors)

Every color in the palette exists in a 12-bit color space because each component can be stored in four bits, totaling 12 bits. As a result, each component can also be represented by one hexadecimal. It's nice to have a palette where the colors don't require 24 bits to be displayed correctly, and three hexadecimal digits are arguably easier to type out and remember than six.