>Unless the AI is 100% offline and locally hosted there's a record there.

Yes, there are these things called "Local LLMs" that run entirely on your machine.

>Most of the time the information you have to share, especially anything verifiable, will be traceable back to you.

Maybe by other mechanisms, but not by this one (writer profiling). The "profile" would just be of the style of the LLM you use.