spawn: Add work instruction + export SessionName

- Export session.Manager.SessionName for spawn.go access
- Add --address alias for --identity in mail inbox/check
- Send explicit work instruction to polecat after spawn
- Add CapturePaneLines and WaitForClaudeReady helpers (unused for now)
- Proper solution filed as gt-hb0 (needs Witness/Deacon AI monitoring)

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

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

internal/tmux/tmux.go

@@ -177,6 +177,18 @@ func (t *Tmux) CapturePaneAll(session string) (string, error) {
 	return t.run("capture-pane", "-p", "-t", session, "-S", "-")
 }
 
+// CapturePaneLines captures the last N lines of a pane as a slice.
+func (t *Tmux) CapturePaneLines(session string, lines int) ([]string, error) {
+	out, err := t.CapturePane(session, lines)
+	if err != nil {
+		return nil, err
+	}
+	if out == "" {
+		return nil, nil
+	}
+	return strings.Split(out, "\n"), nil
+}
+
 // AttachSession attaches to an existing session.
 // Note: This replaces the current process with tmux attach.
 func (t *Tmux) AttachSession(session string) error {
@@ -314,6 +326,30 @@ func (t *Tmux) WaitForShellReady(session string, timeout time.Duration) error {
 	return fmt.Errorf("timeout waiting for shell")
 }
 
+// WaitForClaudeReady polls until Claude's prompt indicator appears in the pane.
+// Claude is ready when we see "> " at the start of a line (the input prompt).
+// This is more reliable than just checking if node is running.
+func (t *Tmux) WaitForClaudeReady(session string, timeout time.Duration) error {
+	deadline := time.Now().Add(timeout)
+	for time.Now().Before(deadline) {
+		// Capture last few lines of the pane
+		lines, err := t.CapturePaneLines(session, 10)
+		if err != nil {
+			time.Sleep(200 * time.Millisecond)
+			continue
+		}
+		// Look for Claude's prompt indicator "> " at start of line
+		for _, line := range lines {
+			trimmed := strings.TrimSpace(line)
+			if strings.HasPrefix(trimmed, "> ") || trimmed == ">" {
+				return nil
+			}
+		}
+		time.Sleep(200 * time.Millisecond)
+	}
+	return fmt.Errorf("timeout waiting for Claude prompt")
+}
+
 // GetSessionInfo returns detailed information about a session.
 func (t *Tmux) GetSessionInfo(name string) (*SessionInfo, error) {
 	format := "#{session_name}|#{session_windows}|#{session_created_string}|#{session_attached}"