test(e2e) : add Playwright setup with product and category CRUD specs

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

package.json

@@ -12,7 +12,10 @@
     "lint": "eslint . --ext .js,.ts,.vue",
     "lint:fix": "npm run lint -- --fix",
     "test": "vitest run",
-    "test:watch": "vitest"
+    "test:watch": "vitest",
+    "test:e2e": "playwright test",
+    "test:e2e:ui": "playwright test --ui",
+    "test:e2e:headed": "playwright test --headed"
   },
   "dependencies": {
     "@nuxtjs/tailwindcss": "^6.14.0",
@@ -26,6 +29,7 @@
   "devDependencies": {
     "@iconify-json/lucide": "^1.2.68",
     "@nuxt/eslint-config": "^1.9.0",
+    "@playwright/test": "^1.58.2",
     "@rushstack/eslint-patch": "^1.12.0",
     "@types/node": "^25.2.1",
     "@typescript-eslint/eslint-plugin": "^8.44.1",