I would say it depends on what kind of text the LLM returns to you and what you do with it. If you're only receiving feedback and suggestions, and making the edits yourself, I would say that the final result is your writing. If you're asking the LLM to do a rewrite, and you're checking its results before sending it off as your own, then that's a bit blurrier... Like, if you gave that task to an actual human, would they need or expect to be credited as a ghost writer?

Personally, I use LLMs for writing assistance as well, but I never ask it to generate text. I only ask it to:

1. Do basic copy editing. I give it a version of my document with prefixed line numbers, and ask it to find any typos, grammatical errors, or "hard to parse" sentences, and then generate a table of lines with issues. I make all of the fixes myself.

2. Do style and sentiment analysis. I previously worked as a tech writer (design docs, test reports, policies, etc...), so my natural style has become incredibly dry. Too dry for what I try to write these days. So I ask the LLMs for feedback on readability, voice, descriptiveness, emotion, etc... Yes, I know they're not actually "performing" reviews, but there must be enough literary and language analysis embedded within the models that they can take my text and return an appropriate response. They provide basically the same feedback that I've received from actual human readers (mostly that my writing is too dry...), but they're obviously a lot faster. I specifically ask it not to provide suggestions for changes to the actual text.