I don't know if there are people who treat turquoise and aqua as distinct, but I certainly treat them as distinct from blue (azure, cobalt) and green. Several of the colors around the mid range in the linked page are not colors I would use the words "blue" or "green" for. That doesn't mean that I have strict rules here; I don't actually know if I would call what you call "cyan" turquoise or blue; ditto plenty of other words like "seafoam." That's kind of my point -- modulo another poster's comment about this being a test of bad monitor calibration, it's really more about language than about color.

I think there's another set of questions here -- why is "blue-green family" a thing in your mind, rather than "blue-yellow family"? Is there a "red-blue family"? "Orange-blue"?

Many Slavic languages do that, as well as Albanian for some reason?

Russian speakers broadly consider sky blue / turquoise / cyan a distinct color right between green and blue

https://en.wikipedia.org/wiki/Blue%E2%80%93green_distinction...

Although the question "is the color distinct and basic or just a shade?" is very subjective. Is pink distinct or a shade of red/purple? Is purple distinct or a shade of red/blue? Is green distinct or a shade of blue? (it's well-known that in Japanese green separated from blue only relatively recently, with very bluish traffic lights and other quirks included)