Hello. I am a documentary/historical linguist and basic colour terminology is one of the things I do a lot of work on. The answer is quite simple, and that's that it varies.

It varies not only from culture to culture, but also from brown to brown. If you picture in your head "pure brown", and if I do the same, we'll probably come up with different hues, to a greater degree than if we both try to picture our idea of "pure red". Brown comes way later in the development of basic colour terminology because it's just a much less salient colour concept than red.

If we're talking Crayola crayon version of brown, which is kinda a dark reddish orange if I'm remembering my crayons correctly, this would usually fall under the same category as your pure red. But other browns may get grouped with your idea of black, or purple if purple is a colour. In one of the language communities I work with, brown things are generally referred to as 'soil' or 'bruise' coloured, depending on the brown. But wet soil is generally referred to by the word I'd translate as "black".

In these groups (speakers of an otherwise undocumented Tibeo-Burman language group), there are only four basic colour terms. We can call them black, white, red, green, but I actually prefer to translate them as dark, bright, warm and cool since that does a better job of addressing the range of colours they cover. In some communities, yellow is starting to develop, but in a number of those it's literally referred to as "baby poop colour", and in others a word is borrowed from a neighbouring language.

In the traditional Chinese view, there were five basic colour terms: black (xuan), white (bai), red (chi), yellow (huang) and greenblue (qing). Today, a number of these (black, red, greenblue) have been replaced with other words. Green today is a separate word, originally developing from a word meaning "leaf", and blue is also another word, developing from the word for "indigo". Black today is derived from a word meaning dark, and actually cognate with the word in the language I work with most closely. The thing is, depending on the brown, it could be classified as almost all of these but white. Dark yellow, dark red, off-black, or something in the greenblue range, could all be identified by a modern English speaker as a shade of brown.

So it's less a matter of "brown is this basic colour term that is an offshoot of red" than that brown covers a whole range of hues in English and even native English speakers will often take more time to identify something as brown or to have some minor disagreement with other native English speakers about where the line is.

If you're curious about this sort of thing, the beginning of the published work on the topic is mostly with Berlin & Kay (1969), and follow up work done by Kay et al, all cited below. There has been a bit of work done on perception, but a lot of what gets spread around about it on the internet is overblown or incorrect. The more interesting work has to do with classification, and a lot of linguists and anthropologists have gone through communities doing tests, such as those with the Munsell colour chips. I've often used paint samples from home improvement stores in my own work, but real-world objects are much better if you want to look at the cultural contexts of different terms.

tl;dr: it varies between cultures and within a single culture between different shades of brown.

References:

• Berlin, Brent and Paul Kay (1969). Basic Color Terms: Their Universality and Evolution. University of California Press.

• Kay, Paul (1975). "Synchronic Variability and Diachronic Change in Basic Color Terms". In: Language in Society 4, pp. 257–270.

• Kay, Paul, Brent Berlin, and William Merrifield (1991). "Biocultural implications of systems of color naming". In: Journal of Linguistic Anthropology 1.1, pp. 12–25.

• Kay, Paul and C K McDaniel (1978). "The Linguistic Significance of the Meanings of Basic Color Terms". In: Language 54.3, pp. 610–646.

(edited to add some references in case ppl are curious)

Thanks, that was very helpful