refactor: unify agent startup with Manager pattern

- Create mayor.Manager for mayor lifecycle (Start/Stop/IsRunning/Status)
- Create deacon.Manager for deacon lifecycle with respawn loop
- Move session.Manager to polecat.SessionManager (clearer naming)
- Add zombie session detection for mayor/deacon (kills tmux if Claude dead)
- Remove duplicate session startup code from up.go, start.go, mayor.go
- Rename sessMgr -> polecatMgr for consistency
- Make witness/refinery SessionName() public for status display

All agent types now follow the same Manager pattern:
  mgr := agent.NewManager(...)
  mgr.Start(...)
  mgr.Stop()
  mgr.IsRunning()
  mgr.Status()

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

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

internal/refinery/manager.go

@@ -58,8 +58,8 @@ func (m *Manager) stateFile() string {
 	return filepath.Join(m.rig.Path, ".runtime", "refinery.json")
 }
 
-// sessionName returns the tmux session name for this refinery.
-func (m *Manager) sessionName() string {
+// SessionName returns the tmux session name for this refinery.
+func (m *Manager) SessionName() string {
 	return fmt.Sprintf("gt-%s-refinery", m.rig.Name)
 }
 
@@ -111,7 +111,7 @@ func (m *Manager) Start(foreground bool) error {
 	}
 
 	t := tmux.NewTmux()
-	sessionID := m.sessionName()
+	sessionID := m.SessionName()
 
 	if foreground {
 		// In foreground mode, we're likely running inside the tmux session
@@ -253,7 +253,7 @@ func (m *Manager) Stop() error {
 
 	// Check if tmux session exists
 	t := tmux.NewTmux()
-	sessionID := m.sessionName()
+	sessionID := m.SessionName()
 	sessionRunning, _ := t.HasSession(sessionID)
 
 	// If neither state nor session indicates running, it's not running