Nature created an aspect of nature separate from itself - we are creatures that should not exist by natural law... We are things that labor under the illusion of having a self

I think the illusion is the perceived separation between us as the rest of the universe which is more cultural than anything. Culture can arguably be described as a natural process in a way, but many cultures out there do not view us as separate from nature showing that we are not inherently separate at a programmed level. The world "nature" and "natural" also inherently biases us towards this perspective as it means everything that is not caused or created by people; and the word is also largely associated with everything around us and out in the universe. So, technically by definition we're separate from nature but are still the same thing thing/process. Kinda like how a lake is not the ocean but are both water.

we are each somebody, when in fact everybody's nobody...

We're definitely something; our identities, however, which are derived from our limited perception of the universe and and our role in it and sense of free will, will always be limited or have a sense of falseness to them as we can never know everything and likely have no free will at all.

I think the honorable thing for our species to do is to deny our programming. Stop reproducing, walk hand in hand into extinction - one last midnight, brothers and sisters opting out of a raw deal.

Whether or not this is the "correct" thing to do is irrelevant; people will continue to reproduce until they die off and the next stage of evolution, AI, eventually continues on to complete the only truly logical thing one can do--destroy the entire universe to prevent more organic processes from coming into existence and saving trillions of organisms from the doom of spending millions of years convincing themselves they have purpose only to endlessly fulfill the needs of their their biological bodies or pay the consequence of suffering even further than what the existential truth of life already brings.

Yes I'm being somewhat tongue-in-cheek btw.