macOS: Add dock badge notification for bell events (#7118)

Resolves #7108

This PR adds visual notification badges to the Ghostty dock icon when
bell events are triggered while the application is in the background.
This complements the existing dock bounce notification, making it easier
for users to notice when a terminal needs attention.


https://github.com/user-attachments/assets/b54c881f-fea8-4085-8614-432d9e5847b9

macos/Sources/App/macOS/AppDelegate.swift

@@ -199,6 +199,7 @@ class AppDelegate: NSObject,
         ]
 
         let center = UNUserNotificationCenter.current()
+
         center.setNotificationCategories([
             UNNotificationCategory(
                 identifier: Ghostty.userNotificationCategory,
@@ -231,6 +232,9 @@ class AppDelegate: NSObject,
         // If we're back manually then clear the hidden state because macOS handles it.
         self.hiddenState = nil
 
+        // Clear the dock badge when the app becomes active
+        self.setDockBadge(nil)
+
         // First launch stuff
         if (!applicationHasBecomeActive) {
             applicationHasBecomeActive = true
@@ -511,6 +515,53 @@ class AppDelegate: NSObject,
     @objc private func ghosttyBellDidRing(_ notification: Notification) {
         // Bounce the dock icon if we're not focused.
         NSApp.requestUserAttention(.informationalRequest)
+
+        // Handle setting the dock badge based on permissions
+        ghosttyUpdateBadgeForBell()
+    }
+
+    private func ghosttyUpdateBadgeForBell() {
+        let center = UNUserNotificationCenter.current()
+        center.getNotificationSettings { settings in
+            switch settings.authorizationStatus {
+            case .authorized:
+                // Already authorized, check badge setting and set if enabled
+                if settings.badgeSetting == .enabled {
+                    DispatchQueue.main.async {
+                        self.setDockBadge()
+                    }
+                }
+
+            case .notDetermined:
+                // Not determined yet, request authorization for badge
+                center.requestAuthorization(options: [.badge]) { granted, error in
+                    if let error = error {
+                        Self.logger.warning("Error requesting badge authorization: \(error)")
+                        return
+                    }
+
+                    if granted {
+                        // Permission granted, set the badge
+                        DispatchQueue.main.async {
+                            self.setDockBadge()
+                        }
+                    }
+                }
+
+            case .denied, .provisional, .ephemeral:
+                // In these known non-authorized states, do not attempt to set the badge.
+                break
+
+            @unknown default:
+                // Handle future unknown states by doing nothing.
+                break
+            }
+        }
+    }
+
+    private func setDockBadge(_ label: String? = "•") {
+        NSApp.dockTile.badgeLabel = label
+        NSApp.dockTile.display()
     }
 
     private func ghosttyConfigDidChange(config: Ghostty.Config) {