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.config.ts

@@ -0,0 +1,31 @@
+import { defineConfig } from "vitest/config";
+import react from "@vitejs/plugin-react";
+import path from "path";
+
+export default defineConfig({
+  plugins: [react()],
+  test: {
+    globals: true,
+    environment: "jsdom",
+    setupFiles: ["./vitest.setup.ts"],
+    include: ["src/**/*.{test,spec}.{ts,tsx}"],
+    exclude: ["node_modules", ".next", "packages"],
+    coverage: {
+      provider: "v8",
+      reporter: ["text", "json", "html"],
+      exclude: [
+        "node_modules/",
+        ".next/",
+        "packages/",
+        "src/**/*.d.ts",
+        "vitest.config.ts",
+        "vitest.setup.ts",
+      ],
+    },
+  },
+  resolve: {
+    alias: {
+      "@": path.resolve(__dirname, "./src"),
+    },
+  },
+});