feat(tauri): update Windows taskbar badge with combined count

The Windows overlay badge now renders a single combined number and
includes an additional “changes” component in the total. This makes
the badge more informative while keeping the icon compact and
legible across small sizes.

- Simplify badge rendering to one circle with centered text
- Extend the Tauri command and frontend call to pass changes count

src/App.svelte

@@ -679,7 +679,7 @@
       repoPath = "";
       status = null;
       lastStatusFingerprint = "";
-      void setSyncBadge(0, 0).catch(() => {});
+      void setSyncBadge(0, 0, 0).catch(() => {});
     }
     branches = [];
     commits = [];
@@ -713,7 +713,7 @@
     repoPath = activeRepoPath;
     lastStatusFingerprint = statusFingerprint(nextStatus);
     upsertRepoTab(activeRepoPath, nextStatus);
-    void setSyncBadge(nextStatus.ahead, nextStatus.behind).catch(() => {});
+    void setSyncBadge(nextStatus.ahead, nextStatus.behind, nextStatus.files.length).catch(() => {});
   }
 
   function errorToMessage(error: unknown): string {

src/lib/git.ts

@@ -37,10 +37,10 @@ export function getStatus(path: string): Promise<GitStatus> {
   return invoke<GitStatus>("get_status", { path });
 }
 
-// Sets the taskbar icon badge to ahead + behind (0 clears it). Windows only — a no-op on
+// Sets the taskbar icon badge to ahead + behind + changed status files (0 clears it). Windows only — a no-op on
 // other platforms, since Windows has no native numeric badge to fall back to.
-export function setSyncBadge(ahead: number, behind: number): Promise<void> {
-  return invoke<void>("set_sync_badge", { ahead, behind });
+export function setSyncBadge(ahead: number, behind: number, changes: number): Promise<void> {
+  return invoke<void>("set_sync_badge", { ahead, behind, changes });
 }
 
 export function listBranches(path: string): Promise<GitBranch[]> {