I think the closing note for closed homework questions should explicitly contain a short notice about not being limited to literal homework, perhaps mentioning other cases.

Yes, it is explained in the provided link in the note, how to post such questions properly. But in my experience, many new posters have not got there yet when starting arguing their question is not homework. Unless some senior community member has previously posted some ready-to-post warning comment, so it is clear already.

It does not help with the user confusion, when the guide link hint looks like it is really all just about homework.

If it was in a short notice directly in the note, it would save all parties from unnecessary and repeated clarifications.

The phrase to be eventually used in the note can be the one in bold "This includes not just questions from actual homework assignments, but also self-study problems, puzzles, etc." from the meta page how-do-i-ask-homework-questions-on-chemistry-stack-exchange