feat: Implement user profile and parent profile button tests

- Added tests for user profile editing, including name changes, image uploads, and password changes.
- Implemented tests for changing the parent PIN with verification code handling.
- Created tests for account deletion with confirmation dialog and email validation.
- Introduced parent profile button tests for both temporary and permanent modes, verifying badge visibility and menu options.
- Updated Playwright configuration to include new test buckets for user profile and parent profile button scenarios.
- Added e2e plans documentation for user profile and parent profile button tests.

frontend/vue-app/e2e/.auth/user-temp-parent.json

@@ -0,0 +1,35 @@
+{
+  "cookies": [
+    {
+      "name": "refresh_token",
+      "value": "rwrt2Ui8ecL_ZSoiWpPY5Ahvp-L9Egbegz_FaYn9KA8",
+      "domain": "localhost",
+      "path": "/api/auth",
+      "expires": 1781620038.006557,
+      "httpOnly": true,
+      "secure": true,
+      "sameSite": "Strict"
+    },
+    {
+      "name": "access_token",
+      "value": "eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJlbWFpbCI6ImUyZUB0ZXN0LmNvbSIsInVzZXJfaWQiOiI4ZTc3OTM1Yi1jYThlLTRiOGYtYmFlMi00NGQyNDA5MjVjODAiLCJ0b2tlbl92ZXJzaW9uIjowLCJleHAiOjE3NzM4NDQ5Mzd9.NHp7pbMRgbO1jamIJBVwlv75OzbTFoOR801C9gTBNEY",
+      "domain": "localhost",
+      "path": "/",
+      "expires": -1,
+      "httpOnly": true,
+      "secure": true,
+      "sameSite": "Strict"
+    }
+  ],
+  "origins": [
+    {
+      "origin": "https://localhost:5173",
+      "localStorage": [
+        {
+          "name": "authSyncEvent",
+          "value": "{\"type\":\"logout\",\"at\":1773844037684}"
+        }
+      ]
+    }
+  ]
+}