I find it helpful to investigate "I did it with an LLM" by imagining that (perhaps without the user's knowledge) the other end was another human, and asking whether that ought to change the answer.
This quickly engages a lot of social circuitry we've already developed when it comes to questions of what constitutes the user truly learning and having skills, what is meritorious, and who deserves most of the credit.
For example:
* If the spell-checker for your paper was secretly another human, that wouldn't become cheating. (Ditto for a calculator.)
* If you prompt "write an introductory paragraph" for a paper and it was actually a human ghostwriter, you'd obviously be cheating.
* If an executive prompts "write a congratulatory e-mail for me" to an LLM, it's not worse than asking a human secretary to do it.
* If you say "I learned kung-fu" while hiring a [robot/human] to kick the spine out of your opponent, you're a liar either way.