If it wanted to: total war using nukes, followed by a nuclear winter. Satellites and drones track and exterminate remaining pockets of anthropic activity.

It doesn't need to have a habitable earth, it just needs atoms.

Atoms are not exactly in short supply

This is science fiction.

How would AI do this?

May as well say AI would send a spaceship to pull an asteroid to earth.

I’m interested in realistic scenarios to justify what these AI psychosis people are genuinely worried about.