Allow selecting path-backed agents in the TUI picker (#33922)

## Why

Opening the agent picker stopped after adding status history whenever path-backed subagents were present, so those agents could not be selected from the picker.

## What changed

- Continue into the picker after rendering status for path-backed subagents.
- Skip duplicate liveness refreshes for path-backed threads and display non-primary agents by their canonical path when available.

## Testing

- Add a snapshot test that opens the picker for a path-backed agent and verifies that selecting it emits `SelectAgentThread` for the expected thread.

GitOrigin-RevId: 1668bb7817ce4e13c91d85c4d7ddab31c04c97b3

codex-rs/tui/src/app/session_lifecycle.rs

@@ -26,7 +26,7 @@ impl App {
             .into_iter()
             .map(|(thread_id, _)| thread_id)
             .collect();
-        for thread_id in path_backed_thread_ids {
+        for thread_id in path_backed_thread_ids.iter().copied() {
             if let Some(channel) = self.thread_event_channels.get(&thread_id)
                 && channel.attachment() == ThreadEventAttachment::Live
             {
@@ -80,7 +80,6 @@ impl App {
                 .add_to_history(super::agent_status_feed::AgentStatusHistoryCell::new(
                     entries,
                 ));
-            return;
         }
 
         let mut thread_ids = self.agent_navigation.tracked_thread_ids();
@@ -90,7 +89,9 @@ impl App {
             }
         }
         for thread_id in thread_ids {
-            if self.side_threads.contains_key(&thread_id) {
+            if path_backed_thread_ids.contains(&thread_id)
+                || self.side_threads.contains_key(&thread_id)
+            {
                 continue;
             }
             if !self
@@ -127,11 +128,19 @@ impl App {
                 }
                 let id = thread_id;
                 let is_primary = self.primary_thread_id == Some(thread_id);
-                let name = format_agent_picker_item_name(
-                    entry.agent_nickname.as_deref(),
-                    entry.agent_role.as_deref(),
-                    is_primary,
-                );
+                let name = entry
+                    .agent_path
+                    .as_deref()
+                    .map(str::trim)
+                    .filter(|agent_path| !is_primary && !agent_path.is_empty())
+                    .map(ToOwned::to_owned)
+                    .unwrap_or_else(|| {
+                        format_agent_picker_item_name(
+                            entry.agent_nickname.as_deref(),
+                            entry.agent_role.as_deref(),
+                            is_primary,
+                        )
+                    });
                 let uuid = thread_id.to_string();
                 SelectionItem {
                     name: name.clone(),

codex-rs/tui/src/app/tests.rs

@@ -1544,6 +1544,41 @@ async fn open_agent_picker_clears_running_hint_from_completed_snapshot() -> Resu
     Ok(())
 }
 
+#[tokio::test]
+async fn open_agent_picker_selects_path_backed_agent() -> Result<()> {
+    let (mut app, mut app_event_rx, _op_rx) = Box::pin(make_test_app_with_channels()).await;
+    let mut app_server = Box::pin(crate::start_embedded_app_server_for_picker(
+        app.chat_widget.config_ref(),
+    ))
+    .await
+    .expect("embedded app server");
+    let thread_id =
+        ThreadId::from_string("00000000-0000-0000-0000-000000000123").expect("valid thread id");
+    app.thread_event_channels
+        .insert(thread_id, ThreadEventChannel::new(/*capacity*/ 1));
+    app.agent_navigation
+        .record_sub_agent_activity(SubAgentActivityDisplay {
+            thread_id,
+            agent_path: "/root/worker".to_string(),
+            is_running_hint: true,
+        });
+
+    Box::pin(app.open_agent_picker(&mut app_server)).await;
+
+    assert_app_snapshot!(
+        "path_backed_agent_picker",
+        render_bottom_popup(&app.chat_widget, /*width*/ 80)
+    );
+    while app_event_rx.try_recv().is_ok() {}
+    app.chat_widget
+        .handle_key_event(KeyEvent::new(KeyCode::Enter, KeyModifiers::NONE));
+    assert_matches!(
+        app_event_rx.try_recv(),
+        Ok(AppEvent::SelectAgentThread(selected_thread_id)) if selected_thread_id == thread_id
+    );
+    Ok(())
+}
+
 #[tokio::test]
 async fn open_agent_picker_refreshes_replay_only_path_backed_liveness() -> Result<()> {
     let mut app = Box::pin(make_test_app()).await;

codex-rs/tui/src/snapshots/codex_tui__app__tests__path_backed_agent_picker.snap

@@ -0,0 +1,10 @@
+---
+source: tui/src/app/tests.rs
+expression: "render_bottom_popup(&app.chat_widget, 80)"
+---
+  Subagents
+  Select an agent to watch. ⌥ + ← previous, ⌥ + → next.
+
+› 1. • /root/worker  00000000-0000-0000-0000-000000000123
+
+  Press enter to confirm or esc to go back