Ground web search answers in query intent

[asim]

Summary

• Preserve web search query intent in model-ready search context.
• Add confidence guidance so weak search-result matches produce explicit refinement requests instead of unsupported answers.
• Require web_search synthesis to cite listed source URLs.

Closes #812
Closes #814

Testing

• go build ./...
• go test ./... -short
• go vet ./...