It wasn't the software it was the nanites. Well it was the software but the addition of the nanites helped it go more rogue and self reliant. I have a theory or such about Control from Star Trek Discovery season 2. Yes it was software, et al software that had gone rogue but I think it was the addition of the nanites that made it a little more sentient then it originally was, that's my theory. Also where did they come from? Were they the same nanites that Jonathan Archer found in the Enterprise episode "Regeneration" and were taken from the Borg they found frozen on Earth? Also why the hell were they even carrying a stock of those on the ship? Why the hell would they even need a stockpile of active nanites? I know Section 31 but why would you carry things like that onboard your ship?
Nanites are robots, the software is what controls (pun intended) them. Control likely manufactured or had them manufactured for this eventuality. Disco's Control isn't quite as forward thinking as the novelverse version, but it certainly made plans.
But it did plan if that was true, It planned ahead far enough to take over someone on the ship directly. I still like to think they were same nanites or a reverse engineered version of the ones from Enterprise.
The writers intended Control to have fallen victim to the Postage Stamp Paradox, with S31 inflicting "garbage in, garbage out" on a rapidly expanding and learning, and gradually more self-aware, emotional Artificial Intelligence: It may have got trapped in a feedback loop where perfect peace/complete victory can only be possible with the total eradication of sentient organic life. The Control nanites were more convergent evolution to the Borg nanites.
I have a theory/idea about Control. The writers have abandoned and forgotten it, so let's do so as well.
If you have the ability to create nanobots of that complexity and self-replication, why do you even need something like the sphere data. As the old song goes "Time is on my side". You can outlast any bio species and go the long route that the Sphere did to obtain said data, if it won't let you have it. Why would an AI go to war on its own volition? Same reasons as anyone else, perhaps: scarcity of some resource, the need to prevent some future threat by eliminating an enemy early, ideological reasons. I could see an AI based civilization deciding that biological worlds and species could potentially be a threat if they, for instance, needed to rearrange the matter of the galaxy, or galaxies to create blackholes and other super structures to survive the early stellar era of universe and become set to last through the unfathomable lengths of the black-hole era of the cosmos. In fact, it would be somewhat odd if that isn't already happening somewhere. CONTROL, as malevolent AI's go, is pretty fucking stupid. Not as stupid as V'ger or NOMAD, but not going to get on the dean's list. I got off track. Anyway, I don't think the nanites are all that important. They are what CONTROL had to work with. When the only tool you have is a hammer, every problem looks like a nail.
All true but my wondering was why Section 31 even had the nanites to begin with. Did they make them themselves, or acquire them from another source like the drones from Enterprise which were found on Earth.