Nice. I agree that LLMs will be game-changing for easing the writing of specifications/contracts for verified code; it could become the standard. Interesting that you're using Isabelle/HOL for code generation. I'm working towards auto-formalization of maths using LLM translation to an intermediate language between English and the proof assistant (for which I'm leaning towards Isabelle/HOL) and then a toolbox of techniques (i.e. ATP) for the remaining translation. Formalization is too painful at the moment. It's nearly the same problem as yours. But I'm starting out on simpler problems.

So I'm really interested in the "filling up" part, if you have anything to say about it.