I think that some of those who like to talk about how humans have "transcended nature" have simply conjured up a false dichotomy
Is it a false dichotomy, or an ambiguity in the meaning of the word 'nature'?
One meaning of 'nature' has nature contrasted with the works of man. Wilderness areas are natural, cities are not.
A different meaning of 'nature' interprets it as referring more generally to our ontological realm. In other words, to everything that belongs to the natural world and that can therefore be studied and understood by the methods appropriate to studying and understanding that world (most notably science).
So on the first interpretation of nature, every human act that results in something happening that wouldn't have happened otherwise, represents 'transcendence' of nature. Or, as popular culture would more likely spin it, the 'desacration' of nature. We often see this kind of thinking in environmentalism.
On the second interpretation, human beings are natural beings, one of the animal species on this planet, and everything that humans do is natural, just as surely as anything that might happen in the absence of human beings. So on this interpretation, it's hard to see how humans could ever 'transcend' nature.
between that which is supposedly "natural" in humans and that which is not
Yeah, that's another interpretation of the word 'nature'.
There's an idea that everything has an innate essence, the expression of which is that thing's particular perfection. The teleological goal of each thing is to realize its perfection. If nature was left to its own devices, then that teleological evolution would be what drives movement and change. But there's also so-called 'violent' change, outside intrusions that knock natural change off its course and divert it to different externally-imposed ends.
I think that vision ultimately derives from Aristotle, by way of medieval Aristotelianism. The Catholic church's philosophical theology still takes it very seriously.
And oddly but interestingly, so does a loud segment of modern environmentalism. Many of our present-day environmentalists wear their secularism on their sleeves and often claim to be atheists, seemingly unaware that their vision of the world is ultimately derived from the medieval Catholic church. It's the source of the idea of humans desacrating nature, 'violently' diverting nature from its (divinely ordained) goal of realizing its own innate perfection, corrupting it to lesser ends imposed by fallen human beings, such as obtaining raw materials, growing food or making money.
in order to achieve an elevated status for humans, as otherwise, they'd seem too ape-like even for their own we-are-merely-animals tastes.
Darwinists have pwide too!
I'm more inclined to think that it's just an unrecognized consequence of the history of ideas. The ways that people think about things today are strongly shaped by how our ancestors thought about things in the past. The past is what provides us with our conceptual vocabulary, so to speak, our intellectual toolkit for how we deal with the world today.