To quote the OP: "How different colors mean different things (Branding-wise or for alerts/errors/warning)"
And, maybe I am wrong about this, but it seems like you've never even heard of color psychology since you seem to think that it's completely unrelated to color theory and that it's a strawman I cooked up out of nowhere. It's even linked in the related section on the wikipage for color theory https://en.wikipedia.org/wiki/Color_psychology
The parent was talking about color harmony (color wheels) and color psychology. This are very much the things the Wikipedia article you linked is about.
Both are indeed pseudo-scientific mumbo-jumbo.
Color model theory is similar to music theory, in the sense that both theories may just be a codification of familiar patterns. That doesn't mean they're not useful.
Color harmony might well be just a codification of familiar patterns. Musical harmony on the other hand is very different. While it certainly has some parts that are rooted in familiarity, especially when it comes to consonance and dissonance of certain intervalls, most of it has a strong physical and physiological basis.
Musical harmony is not purely subjective and this is well studied. Color harmony is not well studied at all and if there is and serious basis - except for historical use - has yet to be been. That’s why I don’t like the word harmony in connection with colors. It just gives the wrong impression.
I don't know enough about the visual arts to know whether color harmony is a subset of color theory. Or if color harmony is even a thing.
You could start with the Wikipedia page to get a quick overview of what color theory really is: https://en.wikipedia.org/wiki/Color_theory
It is not the pseudo-scientific mumbo-jumbo strawman you're ranting against. Color theory makes no subjective judgements on what colors "mean" or should be used for, but instead focuses on the visual properties and perception of color.