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/cmd/mayor.go

@@ -120,6 +120,7 @@ func startMayorSession(t *tmux.Tmux) error {
 
 	// Set environment
 	_ = t.SetEnvironment(MayorSessionName, "GT_ROLE", "mayor")
+	_ = t.SetEnvironment(MayorSessionName, "BD_ACTOR", "mayor")
 
 	// Apply Mayor theme
 	theme := tmux.MayorTheme()
@@ -127,8 +128,8 @@ func startMayorSession(t *tmux.Tmux) error {
 
 	// Launch Claude - the startup hook handles 'gt prime' automatically
 	// Use SendKeysDelayed to allow shell initialization after NewSession
-	// Export GT_ROLE in the command since tmux SetEnvironment only affects new panes
-	claudeCmd := `export GT_ROLE=mayor && claude --dangerously-skip-permissions`
+	// Export GT_ROLE and BD_ACTOR in the command since tmux SetEnvironment only affects new panes
+	claudeCmd := `export GT_ROLE=mayor BD_ACTOR=mayor && claude --dangerously-skip-permissions`
 	if err := t.SendKeysDelayed(MayorSessionName, claudeCmd, 200); err != nil {
 		return fmt.Errorf("sending command: %w", err)
 	}