Reorganize instruction files and document Claude agent registries (#3018)

* Initial plan

* Reorganize instruction files for Claude agent integration

- Add Claude agent integration section to copilot-instructions.md with reference to AGENTS.md
- Simplify .claude/CLAUDE.md to reference copilot-instructions.md
- Move SDK documentation from CLAUDE.md to AGENTS.md
- Add comprehensive section on registries (hooks, slash commands, tool permissions) to AGENTS.md

Co-authored-by: TylerLeonhardt <2644648+TylerLeonhardt@users.noreply.github.com>

* Address PR feedback: add vscode-node handlers and simplify CLAUDE.md

- Add VS Code-Node handlers section documenting askUserQuestionHandler
- Remove unnecessary sentence from CLAUDE.md

Co-authored-by: TylerLeonhardt <2644648+TylerLeonhardt@users.noreply.github.com>

* Address PR feedback: add package.json info and reorganize Claude section

- Add package.json command registration example for slash commands
- Move Claude Agent Integration reference to External Integrations section for better organization

Co-authored-by: TylerLeonhardt <2644648+TylerLeonhardt@users.noreply.github.com>

* Update AGENTS.md

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

* Update AGENTS.md

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

* Update AGENTS.md

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: TylerLeonhardt <2644648+TylerLeonhardt@users.noreply.github.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>