API docs: `/index/message` & `/search` endpoints

[codebestia]

Write apps/ai_agent/docs/api-index-search.md documenting POST /index/message (Weaviate indexing, insert-vs-replace semantics) and GET /search (query parameters, conversationId filtering, empty-collection short-circuit behavior).

Acceptance criteria:

• /index/message's insert-vs-replace decision logic is documented precisely
• /search's query parameters and filter behavior are documented, including the conversationId filter
• Connection-failure behavior (503, per the existing test suite) is documented for both endpoints

[ShantelPeters]

@ShantelPeters has applied to work on this issue as part of the Stellar Wave Program's 7th wave.

HI, i would like to jump on this issue ,kindly assign i am ready to work , i promise deliver as soon as possible

ℹ️ Repo Maintainers: To accept this application, review their application or assign @ShantelPeters to this issue.

[ChuyCode15]

@ChuyCode15 has applied to work on this issue as part of the Stellar Wave Program's 7th wave.

Hi 👋 I'd like to take on this issue. I am committed to delivering a robust, production-grade implementation that adheres to strict clean code principles, separation of concerns, and comprehensive testing. I will invest the necessary time to ensure the solution is efficient and reliable, staying aligned with the estimated timeframe without cutting corners. Could you assign it to me? Thanks!

ℹ️ Repo Maintainers: To accept this application, review their application or assign @ChuyCode15 to this issue.

[drips-wave]

Congratulations, @ChuyCode15! 🎉 Your application was accepted by the repo's maintainers, and the issue is due on July 30, 2026.

🧑‍💻 @ChuyCode15: Please resolve the issue such that the repo's maintainers have enough time to review your contribution before the due date. You'll earn Points for completing the issue on-time, which will make you eligible for a share of the Stellar Wave Program's reward pool.

Warning

When opening a PR, please link it to this issue to ensure it gets tracked accurately. Points are awarded when this issue is marked as completed by the maintainer.

🤠 Repo maintainers: Please keep an eye on the contributor's progress and review their work before the due date. You can manage this issue, including adjusting its complexity and points, here.

🌊 Happy Wave 🌊