feat: Set BD_ACTOR env var when spawning agents (gt-rhfji)

When gt spawns agents (polecats, crew, patrol roles), it now sets the
BD_ACTOR env var so that bd commands (like `bd hook`) know the agent
identity without coupling to gt.

Updated spawn points:
- gt up (mayor, deacon, witness via ensureSession/ensureWitness)
- gt deacon start
- gt witness start
- gt start refinery
- gt mayor start
- Daemon deacon restart
- Daemon lifecycle restart
- Handoff respawn
- Refinery manager start

BD_ACTOR uses slash format (e.g., gastown/witness, gastown/crew/max)
while GT_ROLE may use dash format internally.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

internal/daemon/lifecycle.go

@@ -262,6 +262,9 @@ func (d *Daemon) restartSession(sessionName, identity string) error {
 
 	// Set environment
 	_ = d.tmux.SetEnvironment(sessionName, "GT_ROLE", identity)
+	// BD_ACTOR uses slashes instead of dashes for path-like identity
+	bdActor := identityToBDActor(identity)
+	_ = d.tmux.SetEnvironment(sessionName, "BD_ACTOR", bdActor)
 
 	// Apply theme
 	if identity == "mayor" {
@@ -427,3 +430,36 @@ func (d *Daemon) identityToStateFile(identity string) string {
 		return ""
 	}
 }
+
+// identityToBDActor converts a daemon identity (with dashes) to BD_ACTOR format (with slashes).
+// Examples:
+//   - "mayor" → "mayor"
+//   - "gastown-witness" → "gastown/witness"
+//   - "gastown-refinery" → "gastown/refinery"
+//   - "gastown-crew-max" → "gastown/crew/max"
+func identityToBDActor(identity string) string {
+	switch identity {
+	case "mayor", "deacon":
+		return identity
+	default:
+		// Pattern: <rig>-witness → <rig>/witness
+		if strings.HasSuffix(identity, "-witness") {
+			rigName := strings.TrimSuffix(identity, "-witness")
+			return rigName + "/witness"
+		}
+		// Pattern: <rig>-refinery → <rig>/refinery
+		if strings.HasSuffix(identity, "-refinery") {
+			rigName := strings.TrimSuffix(identity, "-refinery")
+			return rigName + "/refinery"
+		}
+		// Pattern: <rig>-crew-<name> → <rig>/crew/<name>
+		if strings.Contains(identity, "-crew-") {
+			parts := strings.SplitN(identity, "-crew-", 2)
+			if len(parts) == 2 {
+				return parts[0] + "/crew/" + parts[1]
+			}
+		}
+		// Unknown format - return as-is
+		return identity
+	}
+}