refactor: server auth e2e (#7203)

e2e/package.json

@@ -5,8 +5,8 @@
   "main": "index.js",
   "type": "module",
   "scripts": {
-    "test": "npx playwright test",
-    "build": "tsc"
+    "test:web": "npx playwright test",
+    "test:api": "vitest"
   },
   "keywords": [],
   "author": "",
@@ -16,7 +16,11 @@
     "@playwright/test": "^1.41.2",
     "@types/node": "^20.11.17",
     "@types/pg": "^8.11.0",
+    "@types/supertest": "^6.0.2",
+    "@vitest/coverage-v8": "^1.3.0",
     "pg": "^8.11.3",
-    "typescript": "^5.3.3"
+    "supertest": "^6.3.4",
+    "typescript": "^5.3.3",
+    "vitest": "^1.3.0"
   }
 }