Make web-search answers preserve query intent and cite sources

[asim]

Goal
Ensure agent answers that use web_search stay grounded in returned search results and preserve the user's likely intent for product/name queries instead of confidently answering an adjacent generic meaning.

Scope

• Keep existing public tool/API contracts unchanged.
• Improve synthesis/fallback behavior for web_search-backed answers so the answer includes enough source context (titles/URLs or explicit unavailable/no-results state) for users to verify it.
• Add regression coverage for an ambiguous product/name query where the desired result is present or where the agent must ask/qualify rather than drift to a dictionary-style answer.

Acceptance criteria

• CI-verifiable tests show web_search-backed agent answers cite/reflect the returned result set and do not invent or substitute unrelated meanings.
• If results are missing or low-confidence, the answer says so and offers a refinement instead of presenting an unsupported answer.
• No breaking changes to MCP, A2A, REST, webhook, or env-var contracts.