The problem with the Starchild/Reaper AI is that the more you think about it, the more the plot breaks down, such as:
If the Reaper AI controls the reapers and lives in the citadel, why didn't the AI just activate the Citadel relay back in ME1?
If the Reapers have a central intelligence that already resides in the galaxy then what purpose did Sovereign serve?
Are the Indoctrinated also controlled by The Reaper AI or are they bound to the specific reaper that indoctrinates them? The Collectors seem to indicate it's the latter but that in turn makes Saren's plot make no sense and that is on top of whatever the fuck Cerberus was trying to accomplish. Were Cerberus already pawns of the Reapers in ME2 or did that happen after the fact?
Someone earlier mentioned that Cerberus inexplicably becoming a galactic superpower is somewhat explained in game and it is but there are still gaping holes. Sanctuary is supposed to be how they are mass recruiting for their slave army, but sanctuary is only set up 'after' The reapers attack earth and refugees start flooding to the citadel. Their army is established as early as mars and you are killing them by the hundreds before you even get to Sanctuary.
Oh and they somehow did all this in the 6-ish months between Shepard nuking the collectors and the Reapers hitting earth.
The Catalyst isn’t directly launching every new cycle, think of the reapers as basically it’s lawn mowers-it’s trying to see if two forms of grass can co exist(synthetic and organic). Sovereign is like Vigil said, the left behind scout that opens the relay when the time is right.
The indoctrinated are controlled by the reapers-seemingly collectively. Both Saren, TIM, and Kenson from the arrival DLC all seem to obey the reapers as a whole, not an individual reaper. The Collectors themselves are basically sub contracted labor for the reapers. Harbinger and Sovereign seem like “point men” of the reapers-Sovereign to study and begin the next cycle, and Harbinger to directly command the collectors in processing humans/being tsundere for Shepard.
As for why the Catalyst didn’t activate the citadel, that’s not its purpose-it’s purpose is to observe the cycles, not directly intervene. Only when Shepard gets as far as they do does the catalyst determine that a new solution is required.
Remember it and the reapers don’t see themselves as being in conflict with the galaxy-they’re just plucking the tallest grass(to use the yard analogy) and preventing the other grass from completely destroying the yard.
As for Cerberus-on the Kronos station mission-there is one final video log before you get to the VI, it shows the illusive man receiving implants and his assistant discussing Cerberus soldiers receiving enhancements. Also-in the rescue Jacob mission-it’s made clear that Cerberus scientists were being killed at an accelerating rate(especially those that knew anything about its study of indoctrination or collector technology), so clearly Cerberus was preparing for the reaper invasion/getting rid of anyone who wouldn’t stick reaper tech into their skulls willingly or might have a problem with that in general.
In the video log-the illusive man is outright aware the reapers arrival is imminent and wants the Cerberus personnel implanted by that time. So…presumably Cerberus was mass producing soldiers via indoctrination using its secret facilities and ships and technology via the collector base and its other stations/front companies in preparation for the reaper arrival. Does it explain why they become a galactic threat? Not really, but the game does explain at least why they are more than isolated cells now. They had been preparing/gearing up probably before Shepard went through the omega four relay, and their preparations accelerated in the six month timetable afterwards.
Cerberus was yes actually pawns of the reapers-in ME2. The illusive man was canonically already indoctrinated. It was just a slow process, and the unlike Saren or Kenson-Cerberus and TIm were still capable of pursuing their own goals that conflicted with the reapers(hence them attacking sanctuary). The Illusive Man had a mind of his own, but ultimately even his “freely chosen” decisions benefited the reapers and he didn’t have the power to seize control of them.