The copyright office does not determine the standards for copyright. They are an advisory and notary organization.

Only Congress and the courts do. Copyright exists from the moment a work is created, and does not need to be registered with the copyright office.

The law isn't that complicated; if a work was created with a human being with intent, it's probably eligible for copyright protections.

As long as you can convince a court that you did this, the tools you used are not relevant. The vast majority of LLM art falls in this bucket.