feat(polecat): Add shared beads redirect for polecats (gt-cxtu)

When creating a polecat worktree, create a .beads/redirect file pointing
to the rig-level shared beads database. This eliminates git sync overhead
between polecats - they all connect to the same daemon and database.

Architecture:
  gastown/
    .beads/              <- Shared database (created if missing)
    polecats/
      nux/
        .beads/
          redirect       <- Contains "../../.beads"

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

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

internal/polecat/manager.go

@@ -139,6 +139,14 @@ func (m *Manager) Add(name string) (*Polecat, error) {
 		}
 	}
 
+	// Create beads redirect to share rig-level beads database
+	// This eliminates git sync overhead - all polecats use same daemon
+	if err := m.createBeadsRedirect(polecatPath); err != nil {
+		// Non-fatal - polecat can still work with its own .beads/ if needed
+		// Log warning but don't fail the spawn
+		fmt.Fprintf(os.Stderr, "Warning: could not create beads redirect: %v\n", err)
+	}
+
 	// Return polecat with derived state (no issue assigned yet = idle)
 	// State is derived from beads, not stored in state.json
 	now := time.Now()
@@ -513,3 +521,49 @@ func (m *Manager) loadFromBeads(name string) (*Polecat, error) {
 		Issue:     issueID,
 	}, nil
 }
+
+// createBeadsRedirect creates a .beads/redirect file in the polecat directory
+// that points to the rig-level shared beads database. This eliminates the need
+// for git sync between polecats - they all share the same daemon and database.
+//
+// Directory structure:
+//   gastown/
+//     .beads/              <- Shared database (created if missing)
+//     polecats/
+//       nux/
+//         .beads/
+//           redirect       <- Contains "../../.beads"
+func (m *Manager) createBeadsRedirect(polecatPath string) error {
+	// Rig-level beads path
+	rigBeadsPath := filepath.Join(m.rig.Path, ".beads")
+
+	// Ensure rig-level .beads/ exists
+	if _, err := os.Stat(rigBeadsPath); os.IsNotExist(err) {
+		// Initialize rig-level beads if it doesn't exist
+		// This creates the database and config
+		if err := os.MkdirAll(rigBeadsPath, 0755); err != nil {
+			return fmt.Errorf("creating rig beads dir: %w", err)
+		}
+		// Note: bd will auto-initialize when first used
+	}
+
+	// Create polecat .beads directory
+	polecatBeadsPath := filepath.Join(polecatPath, ".beads")
+	if err := os.MkdirAll(polecatBeadsPath, 0755); err != nil {
+		return fmt.Errorf("creating polecat beads dir: %w", err)
+	}
+
+	// Calculate relative path from polecat to rig beads
+	// polecatPath is like: <rig>/polecats/<name>
+	// rigBeadsPath is like: <rig>/.beads
+	// So relative path is: ../../.beads
+	redirectPath := filepath.Join(polecatBeadsPath, "redirect")
+	relativePath := "../../.beads"
+
+	// Write redirect file
+	if err := os.WriteFile(redirectPath, []byte(relativePath+"\n"), 0644); err != nil {
+		return fmt.Errorf("writing redirect file: %w", err)
+	}
+
+	return nil
+}