fix(statusline): ensure crew sessions have correct hook display

Root cause: tmux statusline showed wrong hook for all java crewmembers
because GT_CREW env var wasn't set in tmux session environment.

Changes:
- statusline.go: Add early return in getHookedWork() when identity is empty
  to prevent returning ALL hooked beads regardless of assignee
- crew_at.go: Call SetEnvironment in the restart path so sessions created
  before GT_CREW was being set get it on restart

Fixes gt-zxnr.

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

internal/cmd/crew_at.go

@@ -250,8 +250,22 @@ func runCrewAt(cmd *cobra.Command, args []string) error {
 				Topic:     "restart",
 			})
 
+			// Ensure tmux session environment is set (for gt status-line to read).
+			// Sessions created before this was added may be missing GT_CREW, etc.
+			envVars := config.AgentEnv(config.AgentEnvConfig{
+				Role:             "crew",
+				Rig:              r.Name,
+				AgentName:        name,
+				TownRoot:         townRoot,
+				RuntimeConfigDir: claudeConfigDir,
+				BeadsNoDaemon:    true,
+			})
+			for k, v := range envVars {
+				_ = t.SetEnvironment(sessionID, k, v)
+			}
+
 			// Use respawn-pane to replace shell with runtime directly
-			// Export GT_ROLE and BD_ACTOR since tmux SetEnvironment only affects new panes
+			// Export GT_ROLE and BD_ACTOR in the command since pane inherits from shell, not session env
 			startupCmd, err := config.BuildCrewStartupCommandWithAgentOverride(r.Name, name, r.Path, beacon, crewAgentOverride)
 			if err != nil {
 				return fmt.Errorf("building startup command: %w", err)

internal/cmd/statusline.go

@@ -713,6 +713,12 @@ func getMailPreviewWithRoot(identity string, maxLen int, townRoot string) (int,
 // beadsDir should be the directory containing .beads (for rig-level) or
 // empty to use the town root (for town-level roles).
 func getHookedWork(identity string, maxLen int, beadsDir string) string {
+	// Guard: identity must be non-empty to filter by assignee.
+	// Without identity, the query would return ALL hooked beads regardless of assignee.
+	if identity == "" {
+		return ""
+	}
+
 	// If no beadsDir specified, use town root
 	if beadsDir == "" {
 		var err error