feat(settings): add extension verification browser mode preference

Let users choose whether signed-session verification opens in the
external browser or in-app browser first, with automatic fallback to
the other mode when launch fails.

lib/providers/download_queue_provider.dart

@@ -2098,6 +2098,7 @@ class DownloadQueueNotifier extends Notifier<DownloadQueueState> {
 
     final opened = await openPendingExtensionVerification(
       normalizedExtensionId,
+      browserMode: ref.read(settingsProvider).extensionVerificationBrowserMode,
     );
     if (!opened) return false;
 

lib/providers/settings_provider.dart

@@ -28,6 +28,10 @@ class SettingsNotifier extends Notifier<AppSettings> {
     'album',
     'playlist',
   };
+  static const Set<String> _extensionVerificationBrowserModeValues = {
+    'external_first',
+    'in_app_first',
+  };
 
   final Future<SharedPreferences> _prefs = SharedPreferences.getInstance();
   final FlutterSecureStorage _secureStorage = const FlutterSecureStorage();
@@ -79,6 +83,10 @@ class SettingsNotifier extends Notifier<AppSettings> {
           defaultSearchTab: sanitizedDefaultSearchTab,
           defaultService: loaded.defaultService,
           searchProvider: loaded.searchProvider,
+          extensionVerificationBrowserMode:
+              _normalizeExtensionVerificationBrowserMode(
+                loaded.extensionVerificationBrowserMode,
+              ),
         );
 
         await _runMigrations(prefs);
@@ -270,6 +278,14 @@ class SettingsNotifier extends Notifier<AppSettings> {
     return 'all';
   }
 
+  String _normalizeExtensionVerificationBrowserMode(String value) {
+    final normalized = value.trim().toLowerCase();
+    if (_extensionVerificationBrowserModeValues.contains(normalized)) {
+      return normalized;
+    }
+    return 'external_first';
+  }
+
   String? _sanitizeRetiredBuiltInProviderId(String? providerId) {
     final normalized = providerId?.trim().toLowerCase();
     if (normalized == null || normalized.isEmpty) return providerId;
@@ -557,6 +573,14 @@ class SettingsNotifier extends Notifier<AppSettings> {
     _saveSettings();
   }
 
+  void setExtensionVerificationBrowserMode(String mode) {
+    state = state.copyWith(
+      extensionVerificationBrowserMode:
+          _normalizeExtensionVerificationBrowserMode(mode),
+    );
+    _saveSettings();
+  }
+
   void setLocale(String locale) {
     state = state.copyWith(locale: locale);
     _saveSettings();

lib/providers/track_provider.dart

@@ -686,6 +686,9 @@ class TrackNotifier extends Notifier<TrackState> {
     try {
       final opened = await openPendingExtensionVerification(
         normalizedExtensionId,
+        browserMode: ref
+            .read(settingsProvider)
+            .extensionVerificationBrowserMode,
       );
       if (!opened) return false;