Yea, Jab instead of Lab in ciecam haha. Btw, ciecam is pretty bad predicting highlights, it was designed for SDR to begin with. Lightness formula in ICtCp is more interesting (and here it is "I").
But yea, difficulty of ciecam02 comes from the fact that it tries to work for different conditions, i.e. if usual colorspaces just need to worry about how everything works with one color temperature (usually 5500 or 6500K), ciecam02 tries to predict how colorspace would look like for different tempratures and for different viewing conditions (viewing conditions do not contribute much difference though).
Oh, and of course, ciecam02 defines 3 colorspaces, because it is impossible to arrange ab channels in euclidean space :) TLDR, there is metric de2000 to compare 2 colors, but this metric defines non-euclidean space. While any colorspace tries to bend that metric to fit into euclidean space. So, we have a lot of spaces that try it with different degree of success.
Cam02 is over-engeneered, but it is pretty easy to use, if you just care about cam-ucs colorspace (one of these three) and standard viewing conditions.
If you kinda just wanna see difference between colorspaces, good papers comparing colorspaces have actually nice visual graphs. If you want to compare them for color editing, I've implemented a colorgrading plugin for photoshop: colorplane (ah, kinda ad ;)).
From most interesting spaces, I would say colorspaces, optimized using machine learning are pretty interesting (papers from 2023/2024). But yeah, this means they work using tensorflow, so you need to use batching, when converting from/to RGB. But yeah, what they did, they took CieLab (yes, that old one), used L from it and stretched AB channels to better fit de2000 metric prediction. Basically, like many other colorspaces are designed, just machine learning is cool to minimise errors in half-automatic way. Heh, someday I should write a looong comparison of colorspaces in an easy language with examples :)