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.

docs/launcher_web_api_spec.md

@@ -173,6 +173,9 @@ to the selected installation root, including files in nested directories.
 The scan separately collects stale paths without hashing their contents:
 
 - every file absent from the manifest in `Data/` and `WoW/Data/`
+- every file absent from the manifest in obsolete `Extentions/` and
+  `WoW/Extentions/` directories, including unused subdirectories and the
+  Extentions directory itself when no manifest files require it
 - `WoW.exe` and `*.dll` absent from the manifest directly in the installation
   root or `WoW/` (binary names are matched without case sensitivity)
 - unused Data subdirectories, ordered after their children; the Data roots and
@@ -325,7 +328,8 @@ The automated tests cover:
 - deterministic `buildHash`
 - path normalization used by `buildHash`
 - preservation of user state and unrelated unmanaged files during cleanup
-- removal of unmanaged Data files, unused subdirectories, WoW.exe, and DLLs
+- removal of unmanaged Data files, unused subdirectories, WoW.exe, DLLs, and
+  obsolete Extentions directories
 - preservation of manifest-listed DLLs and WoW.exe
 - cache cleanup behavior
 - safe path resolution