docs(deepagents): fix chat and popup examples and demo availability - #8186

Summary

The Deep Agents framework is authored/docs-only and does not have an agentic-chat Showcase cell. Its CopilotChat route fell back to the shared source-bound page, which rendered an unsupported-feature banner and two missing-snippet boxes.

• Add a Deep Agents-owned CopilotChat guide with complete provider/chat and starter-suggestion examples.
• Explain that the embedded demo is missing while chat remains supported through the existing quickstart runtime connection.
• Add the guide to the authored navigation.
• Cover route selection, rendered HTML, raw Markdown, navigation, and preservation of the source-bound LangGraph guide.

This is a documentation-only fix. It does not add a Showcase integration or change runtime behavior.

Initial CopilotChat validation

• 16 focused tests passed across the Deep Agents chat, route-selection, and link-integrity suites.
• Both exact TSX examples typechecked against @copilotkit/react-core@1.81.0.
• Shell-docs typecheck, focused lint, and git diff --check passed.
• Registry, demo, Angular source, setup, and search data generation passed.
• Production build passed with next build --webpack after data generation.
• Served the production build locally: the HTML route and both .md / .mdx routes return HTTP 200 with the complete examples and no missing-snippet or unsupported-feature notice.

The standard npm run build launcher cannot run in this sandbox because the tsx CLI attempts to open an IPC socket. Content generators were run with Node's --import tsx loader; the search generator's child process used the same loader in a temporary, uncommitted copy. No generator changes are part of this PR.

The full unit suite completed with 587 tests passing and one sandbox-only failure: search-index-build-contract.test.ts invokes the tsx CLI, which fails to open its IPC socket (listen EPERM). The full suite is not claimed as a pass. Live provider-backed Deep Agents chat was not requalified. The accessible recording transcript confirms the reported documentation symptoms; the remaining transcript requires signup.

Risk / rollback

Scoped to the authored Deep Agents chat and popup routes. Shared Showcase-backed guides and runtime behavior are unchanged. Revert the PR's six files to roll back.

November 4 follow-up: CopilotPopup

The related popup report is a distinct uncovered route, not a duplicate chat fix. Direct production HTML still rendered Missing snippet for deepagents::prebuilt-popup and an unavailable-feature notice. Extend this existing PR rather than creating conflicting navigation changes:

• Add a Deep Agents-owned popup guide with a complete v2 provider/popup example, using the quickstart's agent ID and multi-route connection.
• Explain that only the embedded demo is unavailable, and add the popup to the existing authored navigation.
• Cover authored route/navigation selection, usable raw Markdown/rendered HTML, and preservation of the shared source-bound popup guide.

Verification on commit 70a13aad146da0934d02dc03290c50b9dc53398f:

• 13 focused popup/chat/route-selection tests passed.
• The exact popup TSX example typechecked against the branch-pinned @copilotkit/react-core@1.81.0.
• Docs typecheck, focused lint, and whitespace checks passed.
• Registry/demo/Angular/setup/search generation and production webpack build passed. As above, the sandbox's tsx IPC limitation required the Node loader and a temporary uncommitted search-generator launcher change.
• Served production HTML, .md, and .mdx: all HTTP 200 with the complete example and demo-only notice, no missing-snippet or unsupported-feature message.
• Full local suite initially recorded 585 passed, 5 failed tests, and one suite-load error. Four failures and the load error were missing sparse-checkout fixtures; after fetching those unchanged sources, all 6 tests in the three affected suites passed. The existing search-index IPC test remains sandbox-blocked. This is not a clean full-suite pass.
• GitHub CI started on this commit and is pending. Provider-backed popup chat was not retested. No deployment performed.