Implement integration tests with Playwright

package.json

@@ -6,7 +6,9 @@
     "dev": "next dev",
     "build": "next build",
     "start": "prisma migrate deploy && next start",
-    "lint": "eslint"
+    "lint": "eslint",
+    "test:e2e": "playwright test",
+    "test:e2e:ui": "playwright test --ui"
   },
   "dependencies": {
     "@prisma/client": "^6.19.0",
@@ -22,6 +24,7 @@
     "unist-util-visit-parents": "^6.0.2"
   },
   "devDependencies": {
+    "@playwright/test": "^1.57.0",
     "@types/bcryptjs": "^2.4.6",
     "@types/node": "^20",
     "@types/react": "^19",