I guess in that scenario my preference would be to amend the cherry-picked commit's message to include why it was cherry-picked.

The alternative in your case (leaving it as-is, with an issue number) implies that the entire commit addresses that particular issue number, which may not be true. (It may be part of a series of commits for that issue)

This creates a lot of noise on GitHub though. I prefer to put the issue number in the branch name and in the PR description. But for one-off commits, it goes in the commit message.

Yeah, I prefer the issue number in each commit as it makes the commit log more readable to me. But do a decent job of everything else and that is a very small nit-pick.