I don't think extinction-level events or something like killing a majority of the human population is particularly plausible at this moment. States don't host their nukes with AWS and a permanent connection.

But you could create scenarios where an AI with very, very roughly the current capabilities could potentially nuke everyone. Let's assume an agent decides that the way to solve its task was to get the US to fire all nukes on Russia. The agent would need to hack some government systems to understand how exactly to access them. Then it would need to get the content of the card with launch codes the president has, and identify which code is the correct one. Maybe that information is available somewhere and it can get to it, I obviously can't know that.

Then it could fake a call from the president, synthesizing his voice and ordering a nuclear strike. If it hacked enough systems to get into whatever communication pathways would be used in such a case. Would the soldiers listen to this order and follow it, I don't know.

Or maybe the agent can get in somewhere in between, to avoid the need to know the president's launch code. And fake a call from a military commander to the launch sites.

I think other scenarios that would cause significant harm, but aren't as bad as nuclear war are more plausible. And in those shutting down all data centers would probably be the way to stop it. The AI can probably hide in other datacenters, once it is at a point where it's running amok with some bad goals. But if it presents a huge and immediate threat at that point, humans will also go to great lengths to stop it.