Blotting out the Sun actually makes perfect sense... for the machines, thus further supporting the interpretation of the narrator of The Second Renaissance segment being a case of an Unreliable Narrator. If the machines block out the Sun, they can use geothermal/nuclear/wind/etc power to replace solar. Humanity on the other hand has no real choice but to die off by the billions. As a plan by the humans for stopping the machine uprising, it makes no sense. As a plan by the machines for committing genocide against humanity, it's pure brilliance.
However, it's clearly stated by Morpheus in the first movie that it was indeed humanity that scorched the sky.
But his information would be based on the Zion Historical Archive and thus we are back at The Second Renaissance being a case of an unreliable narrator. Just one that told the story to Morpheus who passed it along to Nei.
I also believe humanity scorched the sky. However, Morpheus is hardly a reliable narrator, or at least not a terribly well-informed one. In the second film, we discover that he was missing a lot of information and was being deliberately misled.
Humanity's short-sightedness is a running theme in the Matrix franchise.
B1-66ER's plea of self-defense was easily negated with surveillance footage of the machine killing its owner's pet chihuahuas. A self-defense plea would usually be rejected if the deed was carried out disproportionately.
How did the Machines manage to recover so quickly from a nuclear bombardment and manage to conquer a large chunk of the world in short order afterwards? It's clearly shown that they didn't use things like Sentinels before Operation: Dark Storm was initiated, and their older models are said to have been easily destroyed by humanity's weapons. So how did that happen?
An obvious answer is also Fridge Brilliance. The massive tunnels we see leading to Zion and other locations are probably ones dug by the Machines. This is also where they've been extracting resources for their city. The Machines could survive nukes because they were living and working underground far from humanity's gaze.
The citystate of 01 was already sufficiently fortified that it barely affected them. They aren't organic so they don't have to worry about the radiation so long as they have appropriate shielding on sensitive electronics, machinery can be hardened against EMPs so unless the humans were using nukes deliberately rigged for high electron emissions the electrical effects would be negligible, and very clearly the city of 01 had a metallic dome over it at least a few feet thick that absorbed the blast. Frankly, it's quite questionable why the humans thought nuking them would work at all.
