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/daemon/daemon.go

@@ -847,17 +847,19 @@ func (d *Daemon) restartPolecatSession(rigName, polecatName, sessionName string)
 	}
 
 	// Set environment variables
-	_ = d.tmux.SetEnvironment(sessionName, "GT_ROLE", "polecat")
-	_ = d.tmux.SetEnvironment(sessionName, "GT_RIG", rigName)
-	_ = d.tmux.SetEnvironment(sessionName, "GT_POLECAT", polecatName)
-
-	bdActor := fmt.Sprintf("%s/polecats/%s", rigName, polecatName)
-	_ = d.tmux.SetEnvironment(sessionName, "BD_ACTOR", bdActor)
+	// Use shared RoleEnvVars for consistency across all role startup paths
+	envVars := config.RoleEnvVars("polecat", rigName, polecatName)
 
+	// Add polecat-specific beads configuration
 	beadsDir := filepath.Join(d.config.TownRoot, rigName, ".beads")
-	_ = d.tmux.SetEnvironment(sessionName, "BEADS_DIR", beadsDir)
-	_ = d.tmux.SetEnvironment(sessionName, "BEADS_NO_DAEMON", "1")
-	_ = d.tmux.SetEnvironment(sessionName, "BEADS_AGENT_NAME", fmt.Sprintf("%s/%s", rigName, polecatName))
+	envVars["BEADS_DIR"] = beadsDir
+	envVars["BEADS_NO_DAEMON"] = "1"
+	envVars["BEADS_AGENT_NAME"] = fmt.Sprintf("%s/%s", rigName, polecatName)
+
+	// Set all env vars in tmux session (for debugging) and they'll also be exported to Claude
+	for k, v := range envVars {
+		_ = d.tmux.SetEnvironment(sessionName, k, v)
+	}
 
 	// Apply theme
 	theme := tmux.AssignTheme(rigName)
@@ -870,7 +872,7 @@ func (d *Daemon) restartPolecatSession(rigName, polecatName, sessionName string)
 	// Launch Claude with environment exported inline
 	// Pass rigPath so rig agent settings are honored (not town-level defaults)
 	rigPath := filepath.Join(d.config.TownRoot, rigName)
-	startCmd := config.BuildPolecatStartupCommand(rigName, polecatName, rigPath, "")
+	startCmd := config.BuildStartupCommand(envVars, rigPath, "")
 	if err := d.tmux.SendKeys(sessionName, startCmd); err != nil {
 		return fmt.Errorf("sending startup command: %w", err)
 	}