feat(tauri): add Windows taskbar overlay badge for git sync status

This change introduces a Windows-only taskbar badge that displays the
ahead+behind count as a rendered overlay icon. The UI now updates
the badge whenever the repository sync status changes, and the git
diff commands are adjusted to avoid external diff/text conversion noise.

- Add badge rendering and Tauri command for setting overlay icon
- Wire badge updates into the Svelte app based on git status
- Update git diff invocations to disable ext-diff/textconv

src-tauri/src/main.rs

@@ -1,7 +1,9 @@
 #![cfg_attr(not(debug_assertions), windows_subsystem = "windows")]
 
+mod badge;
 mod git;
 
+use badge::set_sync_badge;
 use git::{
     SearchCancellationState, apply_file_patch, cancel_code_search, cancel_file_history,
     checkout_branch, commit, commit_ai_generate, commit_ai_load, commit_ai_local_models,
@@ -62,7 +64,8 @@ fn main() {
             get_remote_url,
             cred_load,
             cred_save,
-            cred_delete
+            cred_delete,
+            set_sync_badge
         ])
         .run(tauri::generate_context!())
         .expect("error while running tauri application");