I think authorship is linked to the direction of the tool.

Statistical models are everywhere. Digital photos are a good example, nobody questions your authorship when you prompt the camera to capture a picture, while the result comes from a statistical model.

Direction is what gives a work meaning. Just having a llm output something without directing it, is meaningless, it's not a work.

Trying to draw a line at a certain level of involvement seems unnecessary and impossible to me.