Align embed with homepage example

[jbax1899]

Related to #883, following up on the embed presentation delivered there.

Summary

• Match the embed header and introduction to the homepage, including its first prepared answer.
• Keep unavailable TRACE and Report controls disabled without explanatory status text.
• Use the homepage-style question prompt and remove the divider above the live chat.

Verification

• Focused response-footnote and landing-scenario tests: 23 passed via the locally installed tsx binary.
• Web TypeScript check passed via the locally installed tsc binary.
• Embed browser smoke: 3 tests passed; Playwright later reported a 60-second plugin teardown timeout.
• pnpm format:write could not run because pnpm refused the required 11.21.0 signature after registry fetch failures. Local Prettier ran on changed TypeScript files. pnpm review --changed-only remains unrun for the same package-manager issue.

Summary by CodeRabbit

• Updates
  • The embedded page now uses the public header and homepage messaging, and displays a prepared answer with its sources and response details.
  • The prepared answer is separate from visitor chat; Trace and Report controls remain disabled without showing availability messages.
  • The live chat input has updated placeholder text and styling. The embedded page no longer displays the public footer.

[coderabbitai]

📝 Walkthrough

The embed page now displays the homepage’s first prepared answer with shared public branding. The page retains a separate live chat area with a configurable placeholder. Footnote action buttons remain disabled when unavailable, without displaying availability messages.

Changes: Embed Page

Layer / File(s)	Summary
Use homepage prepared answer packages/web/src/pages/EmbedPage.tsx, packages/web/src/data/embedScenario.*	The embed now uses the first landing scenario for its question, response, and metadata. The static embed scenario and its test are removed.
Update embed presentation packages/web/src/pages/EmbedPage.tsx, packages/web/src/components/Chat.tsx, packages/web/src/styles/public-home.css, docs/architecture/embedding.md, test/basic-output-check/embed.spec.ts	The embed adds the public header, updates its copy and live-chat placeholder, and changes its layout styling. Documentation and browser tests reflect the prepared answer and page presentation.
Remove unavailable-action messages packages/web/src/components/CanonicalResponseFootnote.tsx, packages/web/src/components/CanonicalResponseFootnote.test.tsx	Footnote buttons retain their action state but no longer accept or display unavailable-action reasons. Component tests check that these messages are absent.

Priority: ⬇️ Low

Estimated code review effort: 3 (Moderate) | ~20 minutes

Change: Feature

Merge Risk: 🟡 Moderate · up to da381

Header links on the embed page would load full site pages inside the embedding iframe. Open them in a new tab before merging.

Pre-merge checks: 5

Check name	Status	Explanation
Docstring Coverage		No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check. Docstring coverage is scoped to functions touched by this diff. Analyzed 0 functions across 4…
Linked Issues check		Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check		Check skipped because no linked issues were found for this pull request.
Description Check		Check skipped - CodeRabbit’s high-level summary is enabled.
Title check		The title clearly and concisely describes the main change: aligning the embed with the homepage example and presentation.

✨ Finishing Touches

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🧪 Generate unit tests (beta)

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• Autofix · Keep fixing CodeRabbit findings and required CI, and resolving merge conflicts

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_{A rabbit peeks at answers bright,
The homepage now shares its light.
A rounded chat waits below,
Quiet buttons tell what they know.
I nibble docs, then hop from sight.}

_{Comment @coderabbitai help to get the list of available commands.}

[sonarqubecloud]

Quality Gate passed

Issues
1 New issue
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud