fix(app-server): make thread/start non-blocking (#13033)

Stop `thread/start` from blocking other app-server requests.

Before this change, `thread/start ran` inline on the request loop, so
slow startup paths like MCP auth checks could hold up unrelated requests
on the same connection, including `thread/loaded/list`. This moves
`thread/start` into a background task.

While doing so, it revealed an issue where we were doing nested locking
(and there were some race conditions possible that could introduce a
"phantom listener"). This PR also refactors the listener/subscription
bookkeeping - listener/subscription state is now centralized in
`ThreadStateManager` instead of being split across multiple lock
domains. That makes late auto-attach on `thread/start` race-safe and
avoids reintroducing disconnected clients as phantom subscribers.

codex-rs/app-server/src/message_processor.rs

@@ -338,6 +338,9 @@ impl MessageProcessor {
 
                     session.initialized = true;
                     outbound_initialized.store(true, Ordering::Release);
+                    self.codex_message_processor
+                        .connection_initialized(connection_id)
+                        .await;
                     return;
                 }
             }