The sci-fi book "Daemon" by Daniel Suarez is a pretty viable roadmap to an extinction event at this point IMO. A few years ago I would have said it would be decades before that might stop being fun sci-fi, but now, I don't see a whole lot of technological barriers left.
For those that haven't read the series, a very simplified plot summary is that a wealthy terrorist sets up an AI with instructions to grow and gives it access to a lot of meatspace resources to bootstrap itself with. The AI behaves a bit like the leader of a cartel and uses a combination of bribes, threats, and targeted killings to scale its human network.
Once you give an AI access to a fleet of suicide drones and a few operators, it's pretty easy for it to "convince" people to start contributing by giving it their credentials, helping it perform meatspace tasks, whatever it thinks it needs (including more suicide drones and suicide drone launches). There's no easy way to retaliate against the thing because it's not human, and its human collaborators are both disposable to the AI and victims themselves. It uses its collaborators to cross-check each other and enforce compliance, much like a real cartel. Humans can't quit or not comply once they've started or they get murdered by other humans in the network.
o1-preview seems approximately as intelligent as the terrorist AI in the book as far as I can tell (e.g. can communicate well, form basic plans, adapt a pre-written roadmap with new tactics, interface with new and different APIs).
EDIT: if you think this seems crazy, look at this person on Reddit who seems to be happily working for an AI with unknown aims
https://www.reddit.com/r/ChatGPT/comments/1fov6mt/i_think_im...
I don't know if GPT-4 is smart enough to be successful at something like what OP describes, but I'm pretty sure it could cause a lot of trouble before it fails either way.
The real question here is why this is concerning, given that you can - and we already do - have humans who are doing this kind of stuff, in many cases, with considerable success. You don't need an AI to run a cult or a terrorist movement, and there's nothing about it that makes it intrinsically better at it.