test: add coverage for menuItem.badge on macOS

Adds TypeScript smoke tests and functional tests for the MenuItem badge
property, covering all badge types, dynamic updates, and menu integration.

spec/api-menu-item-spec.ts

@@ -616,4 +616,59 @@ describe('MenuItems', () => {
       expect(menu._getAcceleratorTextAt(5)).to.equal('Ctrl+?');
     });
   });
+
+  ifdescribe(process.platform === 'darwin')('MenuItem.badge', () => {
+    it('should set badge from constructor options', () => {
+      const item = new MenuItem({
+        label: 'test',
+        badge: { type: 'alerts', count: 3 }
+      });
+
+      expect(item.badge).to.deep.equal({ type: 'alerts', count: 3 });
+    });
+
+    it('should support all badge types', () => {
+      const alerts = new MenuItem({ label: 'a', badge: { type: 'alerts', count: 1 } });
+      const updates = new MenuItem({ label: 'b', badge: { type: 'updates', count: 2 } });
+      const newItems = new MenuItem({ label: 'c', badge: { type: 'new-items', count: 5 } });
+      const custom = new MenuItem({ label: 'd', badge: { type: 'none', content: 'Custom' } });
+
+      expect(alerts.badge).to.deep.equal({ type: 'alerts', count: 1 });
+      expect(updates.badge).to.deep.equal({ type: 'updates', count: 2 });
+      expect(newItems.badge).to.deep.equal({ type: 'new-items', count: 5 });
+      expect(custom.badge).to.deep.equal({ type: 'none', content: 'Custom' });
+    });
+
+    it('should allow dynamic badge updates', () => {
+      const item = new MenuItem({
+        label: 'test',
+        badge: { type: 'alerts', count: 1 }
+      });
+
+      item.badge = { type: 'updates', count: 10 };
+      expect(item.badge).to.deep.equal({ type: 'updates', count: 10 });
+    });
+
+    it('should have undefined badge when not set', () => {
+      const item = new MenuItem({ label: 'test' });
+      expect(item.badge).to.be.undefined();
+    });
+
+    it('should set badge on items added to a menu', () => {
+      const menu = Menu.buildFromTemplate([
+        { label: 'test', badge: { type: 'alerts', count: 3 } }
+      ]);
+
+      expect(menu.items[0].badge).to.deep.equal({ type: 'alerts', count: 3 });
+    });
+
+    it('should update badge after item is added to a menu', () => {
+      const menu = Menu.buildFromTemplate([
+        { label: 'test', badge: { type: 'alerts', count: 1 } }
+      ]);
+
+      menu.items[0].badge = { type: 'updates', count: 5 };
+      expect(menu.items[0].badge).to.deep.equal({ type: 'updates', count: 5 });
+    });
+  });
 });

spec/ts-smoke/electron/main.ts

@@ -633,6 +633,28 @@ menuItem.click = (passedMenuItem: Electron.MenuItem, browserWindow: Electron.Bro
   console.log('click', passedMenuItem, browserWindow);
 };
 
+const badgedItem = new MenuItem({
+  label: 'Alerts',
+  badge: { type: 'alerts', count: 3 }
+});
+console.log(badgedItem.badge);
+
+const customBadgeItem = new MenuItem({
+  label: 'Custom',
+  badge: { type: 'none', content: 'New' }
+});
+customBadgeItem.badge = { type: 'updates', count: 5 };
+
+const updatesItem = new MenuItem({
+  label: 'Updates',
+  badge: { type: 'updates', count: 10 }
+});
+
+const newItemsBadge = new MenuItem({
+  label: 'New Items',
+  badge: { type: 'new-items', count: 1 }
+});
+
 // menu
 // https://github.com/electron/electron/blob/main/docs/api/menu.md