I profoundly doubt that Section 31 is anywhere near as powerful or widespread as it likes to think it is. Contrary to the absurd fantasies of fiction, the bigger a conspiracy is, the more inevitable its exposure becomes, because there are more opportunities for things to go wrong, more lines of communication to be intercepted, more people who could have second thoughts or be co-opted, etc. The idea of a vast, all-powerful, pervasive conspiracy that nobody knows about is a contradiction in terms. The only way Section 31 could've lasted as long as it has and stayed as well-hidden as it has is by being small and limiting its activities.
So the tendency of some fans to assume that S31 has its talons in every single intelligence operation or ethically questionable action in Federation history is one that should be resisted. The problem with conspiracy theories is that they're based on the lack of evidence for a conspiracy. When you're imagining an unknown menace, your imagination tends to run away and picture it as something huge and supernatural and unbeatable. Usually, if there's any real threat underlying the conspiracy theory at all, then the facts would show it's much less powerful, competent, and expansive and far more vulnerable.
If you don't mind me bringing this long-overdone plot up, my take on Section 31 was that it was never a secret so much as it was deniable. A factor in RL conspiracy theories is that there's whole secret armies, bases, and unlimited resources. About the only "secret" group which ever had that sort of authority was the SS. Ian Fleming created SPECTRE as a miniature version of this but, as we know, that series has its own incredibilities (also, Ian Fleming had it wiped out fairly easily once its existence was exposed).
From what we see of Section 31 in the show and even in the novels, it instead functions more like a license to break the rules. If it was behind the phase cloaking device, it doesn't employ a vast army of Section 31 officers but has Starfleet personnel like Riker and the crew of U.S.S Pegasus. We see this with Julian Bashir as the group "recruits" a man they send on missions that they may or may not actually want to do.
In short, its probably a very small organization. Maybe as few as a dozen individuals. Its authority is probably, ironically, its unquestionability. You can't go over their heads because they answer to no one.
I imagine if Section 31 wanted to create an Android, they wouldn't have a big space station with S31 on a bunch of banners like in a video game but simply find someone like Noonien Soong and make them an offer of unlimited resources. How do they do they get these resources? Criminal activity perhaps, black budgets (which may or may not come from blackmailing politicians) or its own factors.
I think Section 31's relationship to Starfleet Intelligence is closer and darker than people think. Basically, whenever they need something done illegal--they let it fall into S31's hands and if the mission fails or the agents are caught, they're just blamed for it. Disavowed as Mission Impossible would say.
It's why the 25th century ending with their destruction may not be permanent. Not because they're not destroyed but because that may just mean those in power will need someone similar to S31 to do their dirty work.