The copyright office is pretty clear on this if you read: https://www.copyright.gov/ai/Copyright-and-Artificial-Intell....

There is case law surrounding the fact that just because you commission a work to another entity doesn't give you co-authorship, the entity doing the work and making creative decisions is the entity that gets copyright.

In order for you to have co-authorship of the commissioned work you have to be involved and pretty much giving instruction level detail to the real author. The opinion shows many cases that its not the case with how LLM prompts work.

The monkey selfie case is relevant also because since it also solidifies that non-persons cannot claim copyright, that means the LLM cannot claim copyright, and therefore it does not have copyright that can be passed onto the LLM operator.