"the process or practice of using another person's ideas or work and pretending that it is your own"
What I am objecting to is the "another person's" part. An LLM is not a person, it is a tool -- a tool that is trained on other people's work, yes.
If you use a different tool like DeepL, which is also trained on other people's work, to produce text purely from an original prompt you give it (i.e. translate something you wrote yourself), and you put that into your paper... is that then plagiarism as well? If not, what if you use an LLM to do the translation instead, instructing it to act strictly as a 'translation tool'?
It seems to me, the mere act of directly copying the output of an LLM into your own work without a reference cannot be considered plagiarism (in every case), unless LLMs are considered people.
Of course, you can prompt an LLM in a way that copying its output would _definitely_ be plagiarism (i.e., asking it to quote the Declaration of Independence verbatim, and then simply copying that).
So, all I'm saying is: The distinction is not that clear, has nuances, and depends on the context.