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/App.svelte

@@ -63,6 +63,7 @@
     restoreFiles,
     restoreToCommit,
     searchCodeIntroductions,
+    setSyncBadge,
     stageFiles,
     unstageFiles,
   } from "./lib/git";
@@ -656,6 +657,7 @@
       repoPath = "";
       status = null;
       lastStatusFingerprint = "";
+      void setSyncBadge(0, 0).catch(() => {});
     }
     branches = [];
     commits = [];
@@ -689,6 +691,7 @@
     repoPath = activeRepoPath;
     lastStatusFingerprint = statusFingerprint(nextStatus);
     upsertRepoTab(activeRepoPath, nextStatus);
+    void setSyncBadge(nextStatus.ahead, nextStatus.behind).catch(() => {});
   }
 
   function errorToMessage(error: unknown): string {

src/lib/git.ts

@@ -37,6 +37,12 @@ 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
+// 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 listBranches(path: string): Promise<GitBranch[]> {
   return invoke<GitBranch[]>("list_branches", { path });
 }