feat: add settings page and theme toggle in user dropdown

- Settings page with Appearance, Navigation, and Account sections
- Theme toggle (System/Light/Dark) in profile dropdown
- Theme syncs with API preferences on login
- Default room preference syncs with backend

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

lib/core/theme/theme_provider.dart

@@ -1,6 +1,9 @@
+import 'dart:developer' as developer;
+
 import 'package:flutter/material.dart';
 import 'package:riverpod_annotation/riverpod_annotation.dart';
 import 'package:shared_preferences/shared_preferences.dart';
+import 'package:tatlock_ui/core/auth/auth_provider.dart';
 
 part 'theme_provider.g.dart';
 
@@ -17,13 +20,21 @@ enum ThemeSetting {
 }
 
 /// Provider for theme setting state.
+///
+/// Syncs with API preferences when user is authenticated. On login, the theme
+/// from API preferences takes precedence over local storage.
 @riverpod
 class ThemeNotifier extends _$ThemeNotifier {
   static const _prefsKey = 'theme_setting';
 
   @override
   ThemeSetting build() {
+    // Load local setting first for immediate UI
     _loadSavedSetting();
+
+    // Listen for auth state changes to sync from API preferences
+    _syncFromAuthPreferences();
+
     return ThemeSetting.system;
   }
 
@@ -39,6 +50,36 @@ class ThemeNotifier extends _$ThemeNotifier {
     }
   }
 
+  /// Listen to auth state and sync theme from API preferences.
+  void _syncFromAuthPreferences() {
+    ref.listen(authProvider, (_, next) {
+      next.whenData((auth) {
+        final apiTheme = auth.preferences?.theme;
+        if (apiTheme != null && apiTheme.isNotEmpty) {
+          try {
+            final themeSetting = ThemeSetting.values.byName(apiTheme);
+            if (themeSetting != state) {
+              developer.log(
+                'Syncing theme from API: $apiTheme',
+                name: 'theme',
+              );
+              state = themeSetting;
+              // Also persist to local storage for offline use
+              _saveToLocalStorage(themeSetting);
+            }
+          } catch (_) {
+            // Invalid theme value from API, keep current
+          }
+        }
+      });
+    });
+  }
+
+  Future<void> _saveToLocalStorage(ThemeSetting setting) async {
+    final prefs = await SharedPreferences.getInstance();
+    await prefs.setString(_prefsKey, setting.name);
+  }
+
   /// Update theme setting and persist to storage.
   Future<void> setSetting(ThemeSetting setting) async {
     state = setting;