> Turning a natural language specification into web scraping code is exactly the kind of code synthesis that current LLMs can already achieve.

I wish, I have tried. LLM's don't understand the DOM. Unless it is as simple as the address being in element id=address, an LLM is useless for generating scraping code. You are better off with an element picker and some heuristics to generate a selector / xpath query. Now there are some specialized models, I found a paper that takes the DOM tree and fits a vector to each node, but I think they are too much effort for little gain, unless someone integrates them into an open source scraping library so they are easy to use.