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/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[]> {