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/env.ts

@@ -0,0 +1,21 @@
+import { z } from "zod";
+
+const envSchema = z.object({
+  NEXT_PUBLIC_BETTER_AUTH_URL: z.string().url().default("http://localhost:3000"),
+});
+
+/**
+ * Validated public env vars. Uses .default() so missing vars don't throw at
+ * import time (keeps next build + CI safe); values fall back to dev defaults.
+ */
+const parsed = envSchema.safeParse({
+  NEXT_PUBLIC_BETTER_AUTH_URL: process.env.NEXT_PUBLIC_BETTER_AUTH_URL,
+});
+
+export const env = parsed.success
+  ? parsed.data
+  : {
+      NEXT_PUBLIC_BETTER_AUTH_URL: "http://localhost:3000",
+    };
+
+export const isEnvValid = () => parsed.success;