> How do you envision the correctness of these solutions being judged?

By LLMs. I think it's possible for agents to infer whether the user was satisfied or not, at least with my usage pattern. For example if I end the discussion it's a good sign. If I ask follow up question that look like workarounds, it's a bad sign :-)

You could also simply prompt the users whether they were satisfied with the answer they received, possibly incentivizing them with StackOverflow-style gamification.