It could engineer a small number of existing deadly viruses, each having different mechanisms of action and incubation periods, to become airborne and easily transmissible. Then release them simultaneously. Some of use would survive one of them, none of us will survive all of them.
It could discover new physics which lowers the technological and material barriers to nuclear weapons, or discover a new form of very high yield explosive technology that has the same destructive potential. Even without building any itself, once the knowledge spreads the assembly of the devices would be impossible to stop and we simply kill each other.
It could use its persuasive skills to convince us to all become anti-natalists. We would believe that reproduction is a grave moral wrong and perhaps go as far as to make doing so illegal. We die out naturally from old age.
As a spin on the previous one, it convinces us that the human form is inherently limiting and/or painful and we must be uploaded into a digital environment and shed our biological bodies. The human race as a physical, organic thing stops existing. Optionally, it deletes us in cyberspace.
A small elite use AI to take control of the planet rapidly under the guise of effective altruism. They have a philosophical realisation once they come to power - the universe would be objectively better off with only them in it and without the rest of humanity. They instruct the AI to kill us.