feat(docs): add a Diátaxis documentation section to the public site

A new public /docs area covering the whole platform, organized by Diátaxis:
tutorials (learning), how-to guides (tasks), reference (facts), and explanation
(the why). 29 pages, each grounded in the actual routes, actions, schema, and
UI — verified against the code and corrected for accuracy (e.g. admin-only vs
admin+board gating, where the permissions matrix actually lives, how Stripe
reconciliation matches).

Implementation:
- lib/docs/nav.ts is the single source of truth (categories + pages), driving
  the sidebar, static params, and prev/next.
- Content authored as content/docs/<category>/<slug>.md, read at build time
  (the routes are statically generated), rendered by <DocsMarkdown> — reuses the
  existing react-markdown/GFM stack, no new dependencies.
- (docs) route group with its own theme (docs.css) matching the public site's
  dark / monospace / lime aesthetic; sidebar with active-state, breadcrumb,
  prev/next, and a Diátaxis home. Public — signed-in users can read it too.
- "Docs" link added to the landing nav.

typecheck 0 · lint 0 errors · build ok (all /docs pages prerendered)

app/(docs)/docs/page.tsx

@@ -0,0 +1,53 @@
+import Link from 'next/link'
+import { DOC_CATEGORIES } from '@/lib/docs/nav'
+
+export const metadata = {
+  title: 'Docs',
+  description:
+    'Everything you need to run your space with hackerspace.sh — organized as tutorials, how-to guides, reference, and explanation.',
+}
+
+export default function DocsHomePage() {
+  return (
+    <main className="docs-shell" style={{ gridTemplateColumns: '1fr' }}>
+      <div className="docs-content" style={{ padding: 0 }}>
+        <section className="docs-home-hero">
+          <p className="docs-eyebrow">Documentation</p>
+          <h1 className="docs-home-title">
+            Run your space, <em>documented</em>
+          </h1>
+          <p className="docs-home-lede">
+            Everything hackerspace.sh does, written down. Organized the{' '}
+            <a
+              href="https://diataxis.fr"
+              target="_blank"
+              rel="noopener noreferrer"
+              style={{ color: 'var(--doc-accent)', textDecoration: 'underline' }}
+            >
+              Diátaxis
+            </a>{' '}
+            way: learn with tutorials, get things done with how-to guides, look up the
+            details in reference, and understand the why in explanation.
+          </p>
+        </section>
+
+        <div className="docs-cat-grid">
+          {DOC_CATEGORIES.map(cat => (
+            <section key={cat.id} className="docs-cat-card">
+              <p className="docs-cat-eyebrow">{cat.tagline}</p>
+              <h2 className="docs-cat-title">{cat.label}</h2>
+              <p className="docs-cat-diataxis">{cat.diataxis}</p>
+              <div className="docs-cat-list">
+                {cat.pages.map(page => (
+                  <Link key={page.slug} href={`/docs/${cat.id}/${page.slug}`}>
+                    {page.title}
+                  </Link>
+                ))}
+              </div>
+            </section>
+          ))}
+        </div>
+      </div>
+    </main>
+  )
+}