Show Codex background task counts

server/src/session/codex.rs

@@ -137,6 +137,9 @@ impl CodexDriver {
             }
             Some((_, process::Liveness::Dead)) | None => {
                 process::clear(session_dir);
+                // Every child thread lived in the app-server which is gone. Clear adopted open
+                // ids before the replacement process reports its background count.
+                subagents.finish_all();
                 // Requests written to a dead process have no recipient. Put their messages back
                 // in front of the unsent queue so restarting cannot silently lose them.
                 while let Some(message) = state.sent.pop_back() {
@@ -200,6 +203,10 @@ impl CodexDriver {
 }
 
 impl Driver for CodexDriver {
+    fn background_tasks(&self) -> Option<usize> {
+        Some(self.inner.subagents.open_count())
+    }
+
     fn send_user_message(&self, text: String, attachments: Vec<AttachmentRef>) {
         let mut state = self.inner.state.lock().unwrap();
         if state.closed {