fix(tui): hide empty reasoning summaries (#31652)

## Why

Reasoning summaries can contain an empty HTML comment placeholder, `<!--
-->`, when a generated summary part has no prose. The TUI treated that
placeholder as visible summary content, so it leaked into both the
completed conversation history and persisted transcript. Multi-part
empty summaries could also leave later generated status headings visible
as orphaned transcript content.

## What

- Strip the empty reasoning-summary placeholder at the shared
`ReasoningSummaryCell` boundary.
- Suppress the cell when removing placeholders leaves only generated
bold status headings.
- Cover the multi-part placeholder-only shape with a rendering
regression test for both normal history and transcript output.

## How to Test

1. Start Codex TUI with reasoning summaries visible, for example with
`hide_agent_reasoning = false` and `model_reasoning_summary =
"detailed"`.
2. Run a turn that receives an empty generated reasoning-summary part.
3. Confirm that the in-progress status heading may appear while the turn
is running, but the completed history and transcript contain neither
literal `<!-- -->` tokens nor orphaned reasoning headings.
4. Confirm that a reasoning summary with actual prose still renders
normally.

The model output is nondeterministic, so the targeted regression covers
the exact multi-part placeholder shape from the report:

- `just test -p codex-tui
reasoning_summary_block_hides_empty_html_comment_parts`

codex-rs/tui/src/chatwidget/tests/history_replay.rs

@@ -867,7 +867,7 @@ async fn replayed_thread_closed_notification_does_not_exit_tui() {
 }
 
 #[tokio::test]
-async fn replayed_reasoning_item_hides_raw_reasoning_when_disabled() {
+async fn replayed_reasoning_item_preserves_summary_parts_and_hides_raw_reasoning_when_disabled() {
     let (mut chat, mut rx, _op_rx) = make_chatwidget_manual(/*model_override*/ None).await;
     chat.config.show_raw_agent_reasoning = false;
     chat.handle_thread_session(crate::session_state::ThreadSessionState {
@@ -897,7 +897,10 @@ async fn replayed_reasoning_item_hides_raw_reasoning_when_disabled() {
     chat.replay_thread_item(
         AppServerThreadItem::Reasoning {
             id: "reasoning-1".to_string(),
-            summary: vec!["Summary only".to_string()],
+            summary: vec![
+                "**Plan**\n\ndone".to_string(),
+                "**Checking tests**\n\n<!-- -->".to_string(),
+            ],
             content: vec!["Raw reasoning".to_string()],
         },
         "turn-1".to_string(),
@@ -910,7 +913,7 @@ async fn replayed_reasoning_item_hides_raw_reasoning_when_disabled() {
         }
         other => panic!("expected InsertHistoryCell, got {other:?}"),
     };
-    assert!(!rendered.trim().is_empty());
+    assert_eq!(rendered, "• done\n");
     assert!(!rendered.contains("Raw reasoning"));
 }
 
@@ -1047,6 +1050,82 @@ async fn live_reasoning_summary_is_not_rendered_twice_when_item_completes() {
     assert_eq!(rendered.matches("Summary only").count(), 1);
 }
 
+#[tokio::test]
+async fn live_reasoning_summary_drops_empty_parts_without_losing_content() {
+    let (mut chat, mut rx, _op_rx) = make_chatwidget_manual(/*model_override*/ None).await;
+    chat.show_welcome_banner = false;
+
+    chat.handle_server_notification(
+        ServerNotification::TurnStarted(TurnStartedNotification {
+            thread_id: "thread-1".to_string(),
+            turn: AppServerTurn {
+                id: "turn-1".to_string(),
+                items_view: codex_app_server_protocol::TurnItemsView::Full,
+                items: Vec::new(),
+                status: AppServerTurnStatus::InProgress,
+                error: None,
+                started_at: Some(0),
+                completed_at: None,
+                duration_ms: None,
+            },
+        }),
+        /*replay_kind*/ None,
+    );
+    let _ = drain_insert_history(&mut rx);
+
+    for (summary_index, delta) in [
+        (0, "**Plan**\n\ndone"),
+        (1, "**Checking tests**\n\n<!-- -->"),
+    ] {
+        chat.handle_server_notification(
+            ServerNotification::ReasoningSummaryPartAdded(
+                codex_app_server_protocol::ReasoningSummaryPartAddedNotification {
+                    thread_id: "thread-1".to_string(),
+                    turn_id: "turn-1".to_string(),
+                    item_id: "reasoning-1".to_string(),
+                    summary_index,
+                },
+            ),
+            /*replay_kind*/ None,
+        );
+        chat.handle_server_notification(
+            ServerNotification::ReasoningSummaryTextDelta(ReasoningSummaryTextDeltaNotification {
+                thread_id: "thread-1".to_string(),
+                turn_id: "turn-1".to_string(),
+                item_id: "reasoning-1".to_string(),
+                delta: delta.to_string(),
+                summary_index,
+            }),
+            /*replay_kind*/ None,
+        );
+    }
+
+    chat.handle_server_notification(
+        ServerNotification::ItemCompleted(ItemCompletedNotification {
+            thread_id: "thread-1".to_string(),
+            turn_id: "turn-1".to_string(),
+            completed_at_ms: 0,
+            item: AppServerThreadItem::Reasoning {
+                id: "reasoning-1".to_string(),
+                summary: vec![
+                    "**Plan**\n\ndone".to_string(),
+                    "**Checking tests**\n\n<!-- -->".to_string(),
+                ],
+                content: Vec::new(),
+            },
+        }),
+        /*replay_kind*/ None,
+    );
+
+    let rendered = match rx.try_recv() {
+        Ok(AppEvent::InsertHistoryCell(cell)) => {
+            lines_to_single_string(&cell.transcript_lines(/*width*/ 80))
+        }
+        other => panic!("expected InsertHistoryCell, got {other:?}"),
+    };
+    assert_eq!(rendered, "• done\n");
+}
+
 #[tokio::test]
 async fn thread_snapshot_replayed_turn_started_marks_task_running() {
     let (mut chat, mut rx, _op_rx) = make_chatwidget_manual(/*model_override*/ None).await;