feat(labs): production-harden adaptive RAG router

[MHHamdan]

What this PR does

Type of change

• content — new or improved concept, math note, recipe, or pattern
• lab — new or updated lab
• tool-snapshot — refresh a tools/ page for a new version
• recipe — new copy-paste solution
• fix — bug fix (broken code, wrong claim, stale link, etc.)
• docs — documentation improvement (README, CONTRIBUTING, glossary, etc.)
• chore — repo infrastructure (CI, configs, dependencies)

Related issues

Closes #

Checklist

The full PR checklist lives in CONTRIBUTING.md. The high-impact items:

Content

• Page follows the relevant template from CONTRIBUTING.md.
• Voice matches the style guide — no hype words, no corporate filler.
• All non-obvious claims cite a source.
• Any tool-version reference includes a verified as of YYYY-MM-DD note and a primary-source link.

Code (if any)

• Runs end-to-end with only .env populated.
• Notebook outputs stripped (jupyter nbconvert --clear-output --inplace).
• No API keys or personal paths committed.
• Linted with ruff, formatted with black.

Cross-linking

• Linked from any relevant concept page, pattern, or learning path.
• Internal links are relative paths.
• Mermaid diagrams render correctly (preview the PR).

Changelog

• If this PR adds new content or bumps a tool snapshot, CHANGELOG.md has an entry under [Unreleased].

Why (not just what)

Notes for the reviewer