fix(shutdown): Improve gastown shutdown reliability

Fixes #291 - gastown is very hard to kill/shutdown/stop

Changes:
- Add shutdown coordination: daemon checks shutdown.lock and skips
  heartbeat auto-restarts during shutdown to prevent fighting shutdown
- Add orphaned Claude/node process detection in shutdown verification

The daemon's heartbeat now checks for shutdown.lock (created by gt down)
and skips auto-restart logic when shutdown is in progress. This prevents
the daemon from restarting agents that were intentionally killed during
shutdown.

Shutdown verification now includes detection of orphaned Claude/node
processes that may be left behind when tmux sessions are killed but
child processes don't terminate.

internal/daemon/daemon.go

@@ -209,6 +209,14 @@ const recoveryHeartbeatInterval = 3 * time.Minute
 // - Agents with work-on-hook not progressing (GUPP violation)
 // - Orphaned work (assigned to dead agents)
 func (d *Daemon) heartbeat(state *State) {
+	// Skip heartbeat if shutdown is in progress.
+	// This prevents the daemon from fighting shutdown by auto-restarting killed agents.
+	// The shutdown.lock file is created by gt down before terminating sessions.
+	if d.isShutdownInProgress() {
+		d.logger.Println("Shutdown in progress, skipping heartbeat")
+		return
+	}
+
 	d.logger.Println("Heartbeat starting (recovery-focused)")
 
 	// 1. Ensure Deacon is running (restart if dead)
@@ -669,6 +677,15 @@ func (d *Daemon) Stop() {
 	d.cancel()
 }
 
+// isShutdownInProgress checks if a shutdown is currently in progress.
+// The shutdown.lock file is created by gt down before terminating sessions.
+// This prevents the daemon from fighting shutdown by auto-restarting killed agents.
+func (d *Daemon) isShutdownInProgress() bool {
+	lockPath := filepath.Join(d.config.TownRoot, "daemon", "shutdown.lock")
+	_, err := os.Stat(lockPath)
+	return err == nil
+}
+
 // IsRunning checks if a daemon is running for the given town.
 // It checks the PID file and verifies the process is alive.
 // Note: The file lock in Run() is the authoritative mechanism for preventing