Unfortunately, reframing the question completely misses the point of the question.

People have been handling categorical and continuous covariates since waaaaaay before the popularization of intersectionality. I'm quite comfortable with doing so myself, including measuring within-group and between-group variation (including correction for covariates).

Rather, I'm asking for examples of where, clearly, Critical Race Theory prompted tests of some intersectional categorization, because they wanted to know that the division that they were talking about was statistically justified.

As an idea, sure! It's not a remotely new idea. If people were ignoring it in legal circles, because, you know ewwww, math! (even to the point of "okay, Bush is President, not Gore, because ewwwww, math, we can't do statistics to re-enfranchise voters who made obvious mistakes"), and CRT (legal theory) got them to say, "Whoa, wait, I can do a sloppy intuitive analog approximation to some math and get a better answer than if I totally ignore math!", well, at least it's a move in the right direction.

However, what I want is to see examples where CRT is subjecting its theses to stringent evidential tests. Where it actually is (this it would be evidence that they care more about being right than about using a predefined framework), and better yet where it wouldn't have been considered without CRT (if it would anyway, despite CRT not being wrong, it also isn't adding anything, so why bother?).

I'm not saying it's never done--indeed, courts do tend to demand this sort of thing in order to prove a discrimination case if individual accounts aren't sufficient. But most of the CRT I've seen outside of the demands of the legal system (imposed by parts of the legal machinery that CRT is critical of!)--the "new approach to racial justice" type stuff that Delgado and Stefancic talk about--isn't the least bit interested in documenting that, for instance, the intersectional principles are actually useful in any given case.