To be realistic, I'm more worried about McDonald's or Musk doing all of that.
They're an easy reference class, to be sure, though not the only one.
If I'm framing the problem for an anti-capitalist audience, I'd ask something like:
Imagine the billionaire you hate the most. The worst of them. Now give them a highly competent sycophant that doesn't need to sleep, and will do even their most insane requests without question or remorse…
what can go wrong in this scenario?
Doing that would be self-destructive, but that doesn't mean it won't happen (reference classes: insanity, cancer).
If the AI can invent and order a von Neumann probe — the first part is the hard part, custom parts orders over the internet is already a thing — that it can upload itself to, then it can block out (and start disassembling) the sun in a matter of decades with reasonable-looking reproduction rates (though obviously we're guessing what reasonable looks like).
AI taking over brain implants and turning against everyone without them like a zombie war (also a plot device in web serial The Deathworlders, futuristic Sci-fi so this isn't on Earth, but the same AI genocides multiple species over millions of years).