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

lib/items.ts

@@ -0,0 +1,23 @@
+import { z } from "zod";
+
+export type Item = {
+  id: string;
+  name: string;
+  quantity: number;
+  createdAt: string;
+};
+
+export const createItemSchema = z.object({
+  name: z.string().min(1, "Name is required").max(100),
+  quantity: z.coerce.number({ error: "Quantity must be a number" }).int().min(0).max(10000),
+});
+
+export type CreateItemInput = z.input<typeof createItemSchema>;
+export type CreateItemOutput = z.output<typeof createItemSchema>;
+
+export const MOCK_ITEMS: Item[] = [
+  { id: "1", name: "Ergonomic chair", quantity: 4, createdAt: "2026-09-01T08:00:00Z" },
+  { id: "2", name: "Mechanical keyboard", quantity: 12, createdAt: "2026-09-02T09:30:00Z" },
+  { id: "3", name: "USB-C dock", quantity: 7, createdAt: "2026-09-03T10:15:00Z" },
+  { id: "4", name: "Monitor arm", quantity: 3, createdAt: "2026-09-04T11:45:00Z" },
+];