refactor(beads,mail): split large files into focused modules

Break down monolithic beads.go and mail.go into smaller, single-purpose files:

beads package:
- beads_agent.go: Agent-related bead operations
- beads_delegation.go: Delegation bead handling
- beads_dog.go: Dog pool operations
- beads_merge_slot.go: Merge slot management
- beads_mr.go: Merge request operations
- beads_redirect.go: Redirect bead handling
- beads_rig.go: Rig bead operations
- beads_role.go: Role bead management

cmd package:
- mail_announce.go: Announcement subcommand
- mail_check.go: Mail check subcommand
- mail_identity.go: Identity management
- mail_inbox.go: Inbox operations
- mail_queue.go: Queue subcommand
- mail_search.go: Search functionality
- mail_send.go: Send subcommand
- mail_thread.go: Thread operations

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

internal/cmd/mail_check.go

@@ -0,0 +1,92 @@
+package cmd
+
+import (
+	"encoding/json"
+	"fmt"
+	"os"
+
+	"github.com/spf13/cobra"
+	"github.com/steveyegge/gastown/internal/mail"
+	"github.com/steveyegge/gastown/internal/style"
+)
+
+func runMailCheck(cmd *cobra.Command, args []string) error {
+	// Determine which inbox (priority: --identity flag, auto-detect)
+	address := ""
+	if mailCheckIdentity != "" {
+		address = mailCheckIdentity
+	} else {
+		address = detectSender()
+	}
+
+	// All mail uses town beads (two-level architecture)
+	workDir, err := findMailWorkDir()
+	if err != nil {
+		if mailCheckInject {
+			// Inject mode: always exit 0, silent on error
+			return nil
+		}
+		return fmt.Errorf("not in a Gas Town workspace: %w", err)
+	}
+
+	// Get mailbox
+	router := mail.NewRouter(workDir)
+	mailbox, err := router.GetMailbox(address)
+	if err != nil {
+		if mailCheckInject {
+			return nil
+		}
+		return fmt.Errorf("getting mailbox: %w", err)
+	}
+
+	// Count unread
+	_, unread, err := mailbox.Count()
+	if err != nil {
+		if mailCheckInject {
+			return nil
+		}
+		return fmt.Errorf("counting messages: %w", err)
+	}
+
+	// JSON output
+	if mailCheckJSON {
+		result := map[string]interface{}{
+			"address": address,
+			"unread":  unread,
+			"has_new": unread > 0,
+		}
+		enc := json.NewEncoder(os.Stdout)
+		enc.SetIndent("", "  ")
+		return enc.Encode(result)
+	}
+
+	// Inject mode: output system-reminder if mail exists
+	if mailCheckInject {
+		if unread > 0 {
+			// Get subjects for context
+			messages, _ := mailbox.ListUnread()
+			var subjects []string
+			for _, msg := range messages {
+				subjects = append(subjects, fmt.Sprintf("- %s from %s: %s", msg.ID, msg.From, msg.Subject))
+			}
+
+			fmt.Println("<system-reminder>")
+			fmt.Printf("You have %d unread message(s) in your inbox.\n\n", unread)
+			for _, s := range subjects {
+				fmt.Println(s)
+			}
+			fmt.Println()
+			fmt.Println("Run 'gt mail inbox' to see your messages, or 'gt mail read <id>' for a specific message.")
+			fmt.Println("</system-reminder>")
+		}
+		return nil
+	}
+
+	// Normal mode
+	if unread > 0 {
+		fmt.Printf("%s %d unread message(s)\n", style.Bold.Render("📬"), unread)
+		return NewSilentExit(0)
+	}
+	fmt.Println("No new mail")
+	return NewSilentExit(1)
+}