A few researchers in a poorly funded government lab can come up with deadlier viruses in a few years (remember the recent controversy) than what nature engineered in millenia.

Killing one human is easier than converting the entire biosphere.

Would you expect some antibodies and phagocytosis to defeat an intelligently engineered self-replicating nanobot the size of a virus (but which doesn't depend on live cells and without the telltale flaws and tradeoffs of Pandemic-reminiscent"can't kill the host cell too quickly" etc.)?

Well, that depends on what I think the engineering constraints are. It could be that in order to be the size of a virus, self-assembly has to be outsourced. It could be that in order to be resistant to phagocytosis, it needs exotic materials which limit its growth rate and maximal growth.

To me it seems like saying "if you drowned the world in acid, the biosphere could well win the fight in a semi-recognizable form and claim the negentropy for themselves"

It's more "in order to drown the world in acid, you need to generate a lot of acid, and that's actually pretty hard."