test: add Vitest setup with 115 tests (backend + frontend)

backend/vitest.config.ts

@@ -0,0 +1,14 @@
+import { defineConfig } from 'vitest/config';
+
+export default defineConfig({
+  test: {
+    globals: true,
+    environment: 'node',
+    include: ['tests/**/*.test.ts'],
+    coverage: {
+      provider: 'v8',
+      include: ['src/**/*.ts'],
+      exclude: ['src/types/**', 'src/websocket/**'],
+    },
+  },
+});