Ad-hominem (literally: "to the person") requires a person on the other side of the argument. This wasn't made or written by a person, thus ad-hominem does not apply.
If you prompted an LLM to make a PSA that people should brush their teeth, is it a fair to argue that brushing your teeth is bad because an LLM made the argument?
A literal form of "to the machine”: none of the rights that a person has.
Example usage:
“That’s not a rebuttal; it’s an argumentum ad machinam -- you’re rejecting it just because AI wrote it.”
So it's a kind of mechanical recombination of ideas.