I don't know, I'm no lawyer.

However, if I make a drawing in the style of Ghibli, I own the copyright because I made it. I don't know if in Japan, art style is copyrightable.

I don't know if copyright applies to generated content (of any sort) though. It probably does.

The important question here isn't who owns the copyright in the output, but rather whether the output also infringes on somebody else's, and if so, who's liable for that: The company that trained the AI, the one that hosts it as a service, or the user that prompted it.