feat(settings): add dedicated Sync tab with CardDAV contacts integration

- Rename Calendar tab to Synchronization with two sections:
  * Calendar Sync (Google, Apple, CalDAV, ICS)
  * Contact Sync (CardDAV) - NEW
- Add visual tab grouping with CSS separators between sections
- Implement CardDAV account management UI:
  * Add/delete accounts
  * Enable/disable addressbooks
  * Manual sync trigger
  * Connection testing
- Add UX improvements:
  * Status badges (success/error/syncing)
  * Empty states with onboarding
  * Inline help tooltips (prepared)
  * Breadcrumb navigation (prepared)
- Update i18n keys in all 14 locales
- All 109 tests passing

Co-Authored-By: Claude Sonnet 4.5 <noreply@anthropic.com>

public/locales/en.json

@@ -760,7 +760,9 @@
     "tabFamily": "Family Management",
     "tabApiTokens": "API Tokens",
     "tabAccount": "Account",
+    "tabSync": "Synchronization",
     "tabsAriaLabel": "Settings sections",
+    "sectionContactSync": "Contact Synchronization",
     "sectionDesign": "Appearance",
     "sectionAppName": "Application name",
     "sectionModules": "Modules",
@@ -1009,7 +1011,30 @@
     "calendarDisabled": "Calendar disabled",
     "calendarsRefreshed": "Calendars refreshed",
     "deleteAccountConfirm": "Really delete CalDAV account? All synced calendars will be removed.",
-    "lastSync": "Last synced"
+    "lastSync": "Last synced",
+    "cardavTitle": "CardDAV Contacts",
+    "cardavDescription": "Connect multiple CardDAV accounts (iCloud, Nextcloud, Radicale, etc.) and sync your contacts.",
+    "cardavAddAccount": "Add CardDAV Account",
+    "cardavEmptyState": "No CardDAV accounts connected yet. Add your first account to sync contacts.",
+    "cardavNameLabel": "Account name",
+    "cardavNamePlaceholder": "e.g. iCloud, Nextcloud",
+    "cardavUrlLabel": "CardDAV Server URL",
+    "cardavUrlPlaceholder": "https://contacts.icloud.com",
+    "cardavUrlHint": "The base URL of your CardDAV server",
+    "cardavUsernameLabel": "Username",
+    "cardavPasswordLabel": "Password",
+    "cardavPasswordHint": "For iCloud: Use app-specific password from appleid.apple.com",
+    "cardavAccountAdded": "CardDAV account added successfully",
+    "cardavAccountDeleted": "CardDAV account removed",
+    "cardavSyncSuccess": "CardDAV sync successful",
+    "cardavSyncFailed": "CardDAV sync failed",
+    "cardavConnectionFailed": "Connection to CardDAV server failed",
+    "cardavAddressbooksToggle": "Show/hide addressbooks",
+    "cardavRefreshAddressbooks": "Refresh addressbooks",
+    "addressbookEnabled": "Addressbook enabled",
+    "addressbookDisabled": "Addressbook disabled",
+    "addressbooksRefreshed": "Addressbooks refreshed",
+    "deleteCardDAVAccountConfirm": "Really delete CardDAV account? All synced contacts will remain but lose their CardDAV link."
   },
   "login": {
     "tagline": "Family planning. Secure. Privacy-friendly. Open source.",