docs: add Newgate memory pipeline investigation design

[tanakaryotadayo-wq]

Summary

• add a design note for investigating the IDE companion memory pipeline from worker execution to recall injection
• link the design from IDE integration docs
• document the verified gaps that must be proven in runtime order

Resolves #25549

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[gemini-code-assist]

Summary of Changes

Hello, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request introduces a structured investigation plan to validate the end-to-end memory pipeline for the IDE companion. The goal is to systematically verify the execution path from worker boot to recall injection, ensuring that each stage of the pipeline is functional and observable before proceeding with further implementation.

Highlights

• New Design Documentation: Added a comprehensive design note outlining the investigation plan for the Newgate-style memory pipeline, covering the worker-to-memory flow.
• Documentation Integration: Linked the new investigation design document within the existing IDE integration documentation for better discoverability.

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[gemini-code-assist]

Code Review

This pull request adds a new design document detailing the investigation of a Newgate-style worker-to-memory pipeline for the IDE companion, along with a reference to it in the integration index. The document defines a multi-phase approach to verify worker execution, logging, and memory recall. I have no feedback to provide.

_{Note: Security Review has been skipped due to the limited scope of the PR.}