docs(dogfood): rewrite the docs-kit docs site to cover the whole gem

[mhenrixon]

What & why

The dogfood docs site had drifted badly behind the gem — epic #8 shipped Markdown islands, the API-docs kit, the .md twin, /llms.txt, search, MCP, --sync, and more, and almost none of it was documented. This rewrites and extends the site so it documents and demonstrates every capability, with each page dogfooding the gem (prose via md islands, DocsUI::Section/Code, and live component renders).

Builds on the bug-fix work in #43 (already merged) — the docs describe the now-fixed behavior.

Refs #8.

Registry + nav

app/models/doc.rb regrouped into 5 headings — Getting started / Authoring / Reference / AI & tooling / Deploy. nav_registries stays the canonical nav path (I verified a c.nav-lambda "promote groups to headings" approach would render empty subgroup summaries and kept the idiomatic path instead).

New pages

Page	What it does (all live-rendered)
Markdown authoring /docs/markdown	The md island, the single-quoted <<~'MD' convention + why, the full GFM vocabulary rendered live, and how markdown flows into the .md twin
API reference /docs/api	Renders a live DocsUI::Endpoint + FieldTable + ErrorTable + RequestExample (4 client tabs) + JsonResponse, plus api_base_url/api_auth_header/api_clients
AI & agents /docs/ai	The .md twin per page, the Markdown masthead action, /llms.txt + /llms-full.txt, the built-in MCP server, and the AGENTS.md + skill the generator scaffolds
Search /docs/search	Server-rendered search + the ⌘K palette, search_* config, progressive enhancement

Rewrites

• Configuration — the "All options" table is now complete: 28/28 knobs with defaults (was 13), grouped by concern; notes version_badge accepts a String or a callable; nav_registries canonical, c.nav the escape hatch.
• Overview — a current "What you get" covering the whole surface, each feature linking to its page.
• Installation — documents the --sync additive upgrade path.
• Styling & CSS — adds c.code_theme / code_theme_dark / dark_themes, and corrects the theme-name description to the now-graceful degradation (not the old NameError crash — fixed in fix: 25 bugs found while dogfooding the docs site (crashes, .md export, search, config) #43).
• Authoring — expanded building-blocks section links to the dedicated pages instead of duplicating them.

Verification

Rendered every page + .md twin + derived surface end-to-end:

• All 14 registered pages → 200, no runtime errors (the "NameError"/"SyntaxError" strings that appear are documentation prose explaining error behavior, not runtime errors).
• .md twins (/docs/api.md, /docs/markdown.md, /docs/ai.md), /llms.txt, /llms-full.txt, and /docs/search?q=… → all 200.
• Docs pages lint clean under the docs app's omakase config.
• Gem suite unaffected — 538 examples, 0 failures.

How it was built

A capability-map + coverage audit (the same run that found the #43 bugs) produced the page plan; the pages were then authored one-per-agent from the real gem API and each render-verified to 200. Agents caught and fixed several authoring footguns along the way (double-quoted heredocs interpolating #{…}, markdown links inside Callouts rendering literally).

https://claude.ai/code/session_01FPQb6z3YwcKRMbvoJhdxnX