Document warm-process HTTP app lifespans

[Kludex]

Summary

• Explain why a warm Lambda process fails when its adapter restarts the same ASGI lifespan.
• Show a fresh HTTP app factory with Host allowlisting and legacy stateless mode.
• Link the existing troubleshooting error to the deployment guidance.

Fixes #3590

Checks

• Clean English docs build (DOCS_LANGUAGES=en-only scripts/docs/build.sh)
• Claude Code CLI review, including a repeated-lifespan smoke test

AI Disclaimer

This PR was developed with the assistance of either Claude or Codex. I've reviewed and verified the changes.

[chatgpt-codex-connector]

Codex Review Summary

This comment shows the latest Codex review activity on this pull request.

Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-10-11T13:25:11.924383Z	0bc072e	PR opened

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[cubic-dev-ai]

No issues found across 2 files

_{Turn on auto-fix | Re-trigger cubic}

[github-actions]

📚 Documentation preview

Preview	https://pr-3681.mcp-python-docs.pages.dev
Deployment	https://a9afa0d8.mcp-python-docs.pages.dev
Commit	0bc072e
Triggered by	@Kludex
Updated	2026-10-11 13:25:23 UTC

[claude]

Code review found no issues

No high-confidence issues detected in this change.