Update Pattern: Refine AI Code Generation Context pattern

[amburi]

Summary

This PR updates the AI Code Generation Context pattern to make the guidance clearer and more practical for
InnerSource contributors and code owners.

Changes

• Adds a story that illustrates why shared AI context matters when multiple contributors use AI-assisted
  coding tools.
• Renames the suggested repository folder from innersource-ai/ to context-store/.
• Refines the recommended structure into core files and a required contexts/ folder.
• Clarifies the purpose of README.md, PROMPT.md, and ARCHITECTURE.md.
• Updates guidance around existing documentation, token efficiency, and maintenance.
• Adds July 2026 as the latest update date.

[spier]

Sorry @amburi this PR slipped through entirely. My bad!

I left some comments/questions for you. Thank you!

[amburi]

Hi @spier

Thanks for your review. :)

Changelog:

• Renamed the suggested folder to context-store/ to better reflect its purpose as a shared source of project
  context.
• Added a folder tree to make the proposed structure easier to understand at a glance.
• Removed the separate examples folder, since examples should ideally live within the relevant context
  files.
• Refined the structure and naming to make the guidance clearer for contributors and maintainers.