feat(dog): add 'gt dog done' command for dogs to mark themselves idle

Dogs can now reset their own state to idle after completing work:

  gt dog done        # Auto-detect from BD_ACTOR
  gt dog done alpha  # Explicit name

This solves the issue where dog sessions would complete work but remain in
"working" state because nothing processed the DOG_DONE mail. Now dogs can
explicitly mark themselves idle before handing off.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

internal/cmd/dog.go

@@ -182,6 +182,22 @@ Examples:
 	RunE: runDogDispatch,
 }
 
+var dogDoneCmd = &cobra.Command{
+	Use:   "done [name]",
+	Short: "Mark a dog as idle (work complete)",
+	Long: `Mark a dog as idle after completing its work.
+
+Dogs call this command after finishing plugin execution to reset their state
+to idle, allowing them to receive new work dispatches.
+
+If no name is provided, attempts to detect the current dog from BD_ACTOR.
+
+Examples:
+  gt dog done alpha     # Explicit dog name
+  gt dog done           # Auto-detect from BD_ACTOR (e.g., "deacon/dogs/alpha")`,
+	RunE: runDogDone,
+}
+
 func init() {
 	// List flags
 	dogListCmd.Flags().BoolVar(&dogListJSON, "json", false, "Output as JSON")
@@ -212,6 +228,7 @@ func init() {
 	dogCmd.AddCommand(dogCallCmd)
 	dogCmd.AddCommand(dogStatusCmd)
 	dogCmd.AddCommand(dogDispatchCmd)
+	dogCmd.AddCommand(dogDoneCmd)
 
 	rootCmd.AddCommand(dogCmd)
 }
@@ -500,6 +517,34 @@ func runDogStatus(cmd *cobra.Command, args []string) error {
 	return showPackStatus(mgr)
 }
 
+func runDogDone(cmd *cobra.Command, args []string) error {
+	mgr, err := getDogManager()
+	if err != nil {
+		return err
+	}
+
+	var name string
+	if len(args) > 0 {
+		name = args[0]
+	} else {
+		// Try to detect from BD_ACTOR (e.g., "deacon/dogs/alpha")
+		actor := os.Getenv("BD_ACTOR")
+		if actor != "" && strings.HasPrefix(actor, "deacon/dogs/") {
+			name = strings.TrimPrefix(actor, "deacon/dogs/")
+		}
+		if name == "" {
+			return fmt.Errorf("no dog name provided and could not detect from BD_ACTOR")
+		}
+	}
+
+	if err := mgr.ClearWork(name); err != nil {
+		return fmt.Errorf("marking dog %s as done: %w", name, err)
+	}
+
+	fmt.Printf("✓ %s marked as idle (ready for new work)\n", name)
+	return nil
+}
+
 func showDogStatus(mgr *dog.Manager, name string) error {
 	d, err := mgr.Get(name)
 	if err != nil {