feat: refactor mail system to use bd mail backend

- Mail commands (send/inbox/read/delete) now wrap bd mail CLI
- Address translation: mayor/ → mayor, rig/polecat → rig-polecat
- Beads stores messages as type=message issues
- Legacy JSONL mode retained for crew workers (local mail)
- Refinery notifications use new mail interface
- Swarm landing notifications use new mail interface

Closes gt-u1j.6, gt-u1j.12

🤖 Generated with Claude Code
Co-Authored-By: Claude <noreply@anthropic.com>

internal/mail/types.go

@@ -1,4 +1,4 @@
-// Package mail provides JSONL-based messaging for agent communication.
+// Package mail provides messaging for agent communication via beads.
 package mail
 
 import (
@@ -19,8 +19,9 @@ const (
 )
 
 // Message represents a mail message between agents.
+// This is the GGT-side representation; it gets translated to/from beads messages.
 type Message struct {
-	// ID is a unique message identifier.
+	// ID is a unique message identifier (beads issue ID like "bd-abc123").
 	ID string `json:"id"`
 
 	// From is the sender address (e.g., "gastown/Toast" or "mayor/").
@@ -38,14 +39,14 @@ type Message struct {
 	// Timestamp is when the message was sent.
 	Timestamp time.Time `json:"timestamp"`
 
-	// Read indicates if the message has been read.
+	// Read indicates if the message has been read (closed in beads).
 	Read bool `json:"read"`
 
 	// Priority is the message priority.
 	Priority Priority `json:"priority"`
 }
 
-// NewMessage creates a new message with a generated ID.
+// NewMessage creates a new message with a generated ID (for legacy JSONL mode).
 func NewMessage(from, to, subject, body string) *Message {
 	return &Message{
 		ID:        generateID(),
@@ -65,3 +66,88 @@ func generateID() string {
 	rand.Read(b)
 	return "msg-" + hex.EncodeToString(b)
 }
+
+// BeadsMessage represents a message as returned by bd mail commands.
+type BeadsMessage struct {
+	ID          string    `json:"id"`
+	Title       string    `json:"title"`       // Subject
+	Description string    `json:"description"` // Body
+	Sender      string    `json:"sender"`      // From identity
+	Assignee    string    `json:"assignee"`    // To identity
+	Priority    int       `json:"priority"`    // 0=urgent, 2=normal
+	Status      string    `json:"status"`      // open=unread, closed=read
+	CreatedAt   time.Time `json:"created_at"`
+}
+
+// ToMessage converts a BeadsMessage to a GGT Message.
+func (bm *BeadsMessage) ToMessage() *Message {
+	priority := PriorityNormal
+	if bm.Priority == 0 {
+		priority = PriorityHigh
+	}
+
+	return &Message{
+		ID:        bm.ID,
+		From:      identityToAddress(bm.Sender),
+		To:        identityToAddress(bm.Assignee),
+		Subject:   bm.Title,
+		Body:      bm.Description,
+		Timestamp: bm.CreatedAt,
+		Read:      bm.Status == "closed",
+		Priority:  priority,
+	}
+}
+
+// addressToIdentity converts a GGT address to a beads identity.
+//
+// Examples:
+//   - "mayor/" → "mayor"
+//   - "gastown/Toast" → "gastown-Toast"
+//   - "gastown/refinery" → "gastown-refinery"
+//   - "gastown/" → "gastown" (rig broadcast)
+func addressToIdentity(address string) string {
+	// Trim trailing slash
+	if len(address) > 0 && address[len(address)-1] == '/' {
+		address = address[:len(address)-1]
+	}
+
+	// Mayor special case
+	if address == "mayor" {
+		return "mayor"
+	}
+
+	// Replace / with - for beads identity
+	// gastown/Toast → gastown-Toast
+	result := ""
+	for _, c := range address {
+		if c == '/' {
+			result += "-"
+		} else {
+			result = result + string(c)
+		}
+	}
+	return result
+}
+
+// identityToAddress converts a beads identity back to a GGT address.
+//
+// Examples:
+//   - "mayor" → "mayor/"
+//   - "gastown-Toast" → "gastown/Toast"
+//   - "gastown-refinery" → "gastown/refinery"
+func identityToAddress(identity string) string {
+	if identity == "mayor" {
+		return "mayor/"
+	}
+
+	// Find first dash and replace with /
+	// gastown-Toast → gastown/Toast
+	for i, c := range identity {
+		if c == '-' {
+			return identity[:i] + "/" + identity[i+1:]
+		}
+	}
+
+	// No dash found, return as-is with trailing slash
+	return identity + "/"
+}