Clean obsolete Extentions during client synchronization

Include the prepared cleanup of both client roots while preserving manifest-listed files and unrelated user state. Verified on Windows through FVM: full formatting and analysis, all 76 tests, production dry run, x64 build and DSA signature verification.

test/features/launcher/application/client_sync_use_case_test.dart

@@ -169,7 +169,12 @@ void main() {
       addTearDown(() => root.delete(recursive: true));
       final service = GameInstallationService();
       final retained = ['MoonWell.exe', 'Data/common.MPQ', 'required.dll'];
-      final obsolete = ['Data/old/patch.MPQ', 'WoW.exe', 'unused.DLL'];
+      final obsolete = [
+        'Data/old/patch.MPQ',
+        'WoW.exe',
+        'unused.DLL',
+        'Extentions/bin/extension.dll',
+      ];
       for (final path in [
         ...retained,
         ...obsolete,
@@ -217,7 +222,12 @@ void main() {
         contains(ClientSyncStage.removingStaleFiles),
       );
       expect(api.downloadedPaths, isEmpty);
-      for (final path in [...obsolete, 'Data/old']) {
+      for (final path in [
+        ...obsolete,
+        'Data/old',
+        'Extentions/bin',
+        'Extentions',
+      ]) {
         expect(
           await FileSystemEntity.type(
             service.resolveClientPath(root.path, path),

test/features/launcher/data/game_installation_service_test.dart

@@ -77,6 +77,8 @@ void main() {
           'WoW/WoW.exe',
           'WoW/old.dll',
           'WoW/Data/old.MPQ',
+          'Extentions/bin/extension.dll',
+          'WoW/Extentions/old.txt',
         ];
         final untouchedPaths = [
           'Cache/cache.bin',
@@ -105,6 +107,9 @@ void main() {
         await Directory(
           service.resolveClientPath(rootDirectory.path, 'Data/unused/nested'),
         ).create(recursive: true);
+        await Directory(
+          service.resolveClientPath(rootDirectory.path, 'Extentions/empty'),
+        ).create(recursive: true);
         final manifest = await _manifestForPaths(
           service,
           rootDirectory,
@@ -129,6 +134,10 @@ void main() {
             'Data/empty',
             'Data/unused/nested',
             'Data/unused',
+            'Extentions/bin',
+            'Extentions/empty',
+            'Extentions',
+            'WoW/Extentions',
           ]),
         );
         for (final path in snapshot.stalePaths) {