refactor: update managers to use RoleEnvVars

Consolidates all role startup code to use the shared RoleEnvVars()
function, ensuring consistent env vars across tmux SetEnvironment
and Claude startup command exports.

Updated:
- Mayor manager
- Deacon startup (daemon.go)
- Witness manager
- Refinery manager
- Polecat startup (daemon.go)
- BuildPolecatStartupCommand, BuildCrewStartupCommand helpers

This ensures all agents receive the same identity env vars regardless
of startup path.

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

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

internal/refinery/manager.go

@@ -186,17 +186,23 @@ func (m *Manager) Start(foreground bool) error {
 	}
 
 	// Set environment variables (non-fatal: session works without these)
-	_ = t.SetEnvironment(sessionID, "GT_RIG", m.rig.Name)
-	_ = t.SetEnvironment(sessionID, "GT_REFINERY", "1")
-	_ = t.SetEnvironment(sessionID, "GT_ROLE", "refinery")
-	_ = t.SetEnvironment(sessionID, "BD_ACTOR", bdActor)
+	// Use shared RoleEnvVars for consistency across all role startup paths
+	envVars := config.RoleEnvVars("refinery", m.rig.Name, "")
 
-	// Set beads environment - refinery uses rig-level beads (non-fatal)
+	// Add refinery-specific flag
+	envVars["GT_REFINERY"] = "1"
+
+	// Add beads environment - refinery uses rig-level beads
 	// Use ResolveBeadsDir to handle both tracked (mayor/rig) and local beads
 	beadsDir := beads.ResolveBeadsDir(m.rig.Path)
-	_ = t.SetEnvironment(sessionID, "BEADS_DIR", beadsDir)
-	_ = t.SetEnvironment(sessionID, "BEADS_NO_DAEMON", "1")
-	_ = t.SetEnvironment(sessionID, "BEADS_AGENT_NAME", fmt.Sprintf("%s/refinery", m.rig.Name))
+	envVars["BEADS_DIR"] = beadsDir
+	envVars["BEADS_NO_DAEMON"] = "1"
+	envVars["BEADS_AGENT_NAME"] = envVars["BD_ACTOR"]
+
+	// Set all env vars in tmux session (for debugging) and they'll also be exported to Claude
+	for k, v := range envVars {
+		_ = t.SetEnvironment(sessionID, k, v)
+	}
 
 	// Apply theme (non-fatal: theming failure doesn't affect operation)
 	theme := tmux.AssignTheme(m.rig.Name)