It’s not the style itself but the use of the art to train the model that outputs the style. Anime as a style is not copyrightable. The work anime artists create is copyrightable. Specifically, if you take their copyrighted work and feed it into a machine to extract the artistic expressions that characterize anime to make new art, is your usage of their art in that process fair use?
Fair Use 4th Factor:
This factor considers whether the use could harm the copyright holders market for the original work.
If the use is research it’s fine. If the use is providing a public non-commercial model then it is somewhat harmful as their work is devalued. If the goal is to compete with them it is very harmful. Therefore, since we’re talking about the last two use cases, I argue fair use does not apply. Others maintain it does as maybe you do.
If it’s not fair use then it would be infringing on that particular copyright holder.
As you know, anime art is a spectrum with “How to Draw Manga for Kids” at the bottom and studio quality at the top. People pick and choose the art to train on not just because of the style but also the quality and consistency of their work. That’s why you might choose a specific artist to base a model on even though their style is just “anime”.