As someone who has dabbled in AI generated crosswords I found that providing samples of "good crossword clues" (which I curated from historical NYT monday puzzles) as part of the LLM context helped tremendously in generating better clues.
There was also a Show HN for a generative AI crossword puzzle system a few months ago so I'll include what I mentioned there:
Part of the deep satisfaction in solving a crossword puzzle is the specificity of the answer. It's far more gratifying to answer a question with something like "Hawking" then to answer with "scientist", or answering with "mandelbrot" versus "shape".
So ideally, you want to lean towards "specificity" wherever possible, and use "generics" as filler.
Link: