feat(testing): implement vitest test suite

Add comprehensive testing infrastructure with vitest, React Testing
Library, and jsdom. Includes tests for:

- Utility functions (cn, isChromeBrowser, date formatting, JSON utils)
- Variable detection module (7 pattern types, conversion, false positives)
- API routes (health check, user registration with validation/auth)

127 tests passing covering critical functionality.

vitest.setup.ts

@@ -0,0 +1,89 @@
+import "@testing-library/jest-dom";
+import { vi } from "vitest";
+
+// Mock environment variables
+process.env.NEXTAUTH_SECRET = "test-secret";
+process.env.NEXTAUTH_URL = "http://localhost:3000";
+process.env.DATABASE_URL = "postgresql://test:test@localhost:5432/test";
+
+// Mock next/navigation
+vi.mock("next/navigation", () => ({
+  useRouter: () => ({
+    push: vi.fn(),
+    replace: vi.fn(),
+    refresh: vi.fn(),
+    back: vi.fn(),
+    forward: vi.fn(),
+    prefetch: vi.fn(),
+  }),
+  useSearchParams: () => new URLSearchParams(),
+  usePathname: () => "/",
+  useParams: () => ({}),
+  redirect: vi.fn(),
+  notFound: vi.fn(),
+}));
+
+// Mock next/headers
+vi.mock("next/headers", () => ({
+  cookies: () => ({
+    get: vi.fn(),
+    set: vi.fn(),
+    delete: vi.fn(),
+  }),
+  headers: () => new Headers(),
+}));
+
+// Mock next-intl
+vi.mock("next-intl", () => ({
+  useTranslations: () => (key: string) => key,
+  useLocale: () => "en",
+  getTranslations: () => Promise.resolve((key: string) => key),
+}));
+
+// Mock Prisma client
+vi.mock("@/lib/db", () => ({
+  db: {
+    user: {
+      findUnique: vi.fn(),
+      findFirst: vi.fn(),
+      findMany: vi.fn(),
+      create: vi.fn(),
+      update: vi.fn(),
+      delete: vi.fn(),
+      count: vi.fn(),
+    },
+    prompt: {
+      findUnique: vi.fn(),
+      findFirst: vi.fn(),
+      findMany: vi.fn(),
+      create: vi.fn(),
+      update: vi.fn(),
+      delete: vi.fn(),
+      count: vi.fn(),
+    },
+    category: {
+      findUnique: vi.fn(),
+      findFirst: vi.fn(),
+      findMany: vi.fn(),
+      create: vi.fn(),
+      update: vi.fn(),
+      delete: vi.fn(),
+    },
+    $queryRaw: vi.fn(),
+    $executeRaw: vi.fn(),
+    $transaction: vi.fn(),
+  },
+}));
+
+// Mock config
+vi.mock("@/lib/config", () => ({
+  getConfig: vi.fn(() =>
+    Promise.resolve({
+      auth: {
+        allowRegistration: true,
+        providers: [],
+      },
+      features: {},
+    })
+  ),
+}));