I am trying a similar spec driven development idea in a project I am working on. One big difference is that my specifications are not formalized that much. Tney are in plain language and are read directly by the LLM to convert to code. That seems like the kind of thing the LLM is good at. One other feature of this is that it allows me to nudge the implmentation a little with text in the spec outside of the formal requirements. I view it two ways, as spec-to-code but also as a saved prompt. I haven't spent enough time with it to say how successfuly it is, yet.
Do you save these "prompts" so you can improve, and in turn improve the code. to me Spec Driven Development is more than a spec to generate code, structured or not.