Well,
it's not as simple as that.
Plagiarism
the process or practice of using another person's ideas or work and pretending that it is your own
Copying and pasting from an AI is not subject to copyright issues in many cases. In the case of the OP he is not simply copying and pasting something that the AI is making up, in order for the AI to produce that text he has had to give it a source of information from where the text has been generated. There is no plagiarism in the sense of the Cambridge dictionary and there is no copyright problem.
I'm going to strongly disagree with you here. I'd argue the Cambridge dictionary's reference to a "person" is outdated. So I'm going to follow a more modern definition, including verbal diarrhea made up by chatbots.
The copyright part is different, usually that's not a problem unless the copyright owner chases you down. But the chatbots themselves could very well be violating copyright laws on a massive scale. They must have used almost anything ever written as input, and I bet they didn't get permission from millions of different authors to reproduce it.