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/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) {