fix Claude secondary pane copy + false "session exited"

Two things surfaced in the secondary pane: the tab said "session 1"
while the banner said "secondary 1" — now both say "session N". And the
banner showed "session exited" right after starting, even though Claude
was alive: a transient tmux client process can exit during spawn while
the session itself is fine. pane.exit now verifies via `tmux has-session`
and only reports exited when the session is actually gone.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

lib/builtin/claude/src/tmux_session.dart

@@ -24,6 +24,14 @@ Future<void> killSession(String name) async {
   await tmuxRunner([..._socket, 'kill-session', '-t', name]);
 }
 
+/// Whether [name] is a live session on the clide socket. Used to suppress
+/// a spurious "session exited" when a transient tmux client process exits
+/// but the session itself is fine (T-149 follow-up).
+Future<bool> hasSession(String name) async {
+  final r = await tmuxRunner([..._socket, 'has-session', '-t', name]);
+  return r.exitCode == 0;
+}
+
 /// Return the names of all sessions currently alive on the clide
 /// socket. Empty list if the server is not running.
 Future<List<String>> listClideSessions() async {