feat: close remaining gaps — middleware, demo wiring, error UX, env validation

- Auth: middleware.ts guards /protected via better-auth session cookie;
  protected page reads session server-side (auth.api.getSession)
- Demo wiring (app/demo + components/demo): react-markdown + remark-gfm +
  shiki CodeBlock, RHF+zod form with react-query mutation + sonner toast,
  react-table items list (legacy API, table v9), /api/items GET+POST
  (zod v4 coercion, schema in lib/items.ts shared with unit tests)
- Error UX: app/error.tsx (retry + digest), not-found.tsx (404), loading.tsx
- Env: lib/env.ts zod-validated (no import-time throw), .env.example sync
  (NEXT_PUBLIC_BETTER_AUTH_URL), auth-client uses env
- Tooling: @vitest/coverage-v8 (test:coverage works), tsconfig cleanup
  (drop .next/dev/dev/types artifact), README rewrite, demo e2e specs

app/loading.tsx

@@ -0,0 +1,10 @@
+export default function Loading() {
+  return (
+    <div className="flex flex-1 items-center justify-center p-8" role="status">
+      <div className="flex items-center gap-3 text-sm text-muted-foreground">
+        <span className="size-4 animate-spin rounded-full border-2 border-foreground/20 border-t-foreground" />
+        Loading…
+      </div>
+    </div>
+  );
+}