Proper refactoring with an llm requires full testing coverage and, by the time you do all that, is the refactoring really necessary? I prefer 100% stability. If you're refactoring the because it's poorly structured and unreadable, that’s okay.. LLMs can help understand it.
In my use of llms, i find it’s actually much easier to rebuild something from scratch rather than refactoring flawed code. It’s much less likely to inherit strange assumptions and code smells that way.
With all that said, the one prompt I do use when refactoring is to tell the llm to do a lossless refactor and then follow up with a "was this really lossless"? It's not foolproof. LLM's love to lie.