Keep side conversations open when switching threads (#35011)

## What changed

- Add a configurable `toggle_side_conversation` TUI action, bound to `ctrl-/` by default, to switch between a side conversation and its parent without closing either.
- Show the active binding in the footer and distinguish switching from closing with `ctrl-c`.
- Allow starting a replacement side conversation from the parent, while cleaning up the previous side thread and preserving it if cleanup fails.
- Clean up retained side conversations when shutting down the current thread.

## Testing

- Cover shortcut remapping, conflicts, and compatibility with existing `ctrl-/` and `ctrl-7` bindings.
- Cover side-thread replacement and footer states for both the parent and side conversation.

GitOrigin-RevId: a621c21e1c45ba73197d59750b2e05efa5ee1081

codex-rs/tui/src/chatwidget/snapshots/codex_tui__chatwidget__tests__side_context_label_preserves_status_line.snap

@@ -6,4 +6,4 @@ expression: terminal.backend()
 "                                                                                "
 "› Check recently modified functions for compatibility                           "
 "                                                                                "
-"  gpt-5.6-sol                         Side from main thread · Ctrl+C to return  "
+"  gpt-5.6-sol   Side from main thread · ctrl + / to switch · ctrl + c to close  "

codex-rs/tui/src/chatwidget/snapshots/codex_tui__chatwidget__tests__side_context_label_shows_hidden_side.snap

@@ -0,0 +1,9 @@
+---
+source: tui/src/chatwidget/tests/side.rs
+expression: terminal.backend()
+---
+"                                                                                "
+"                                                                                "
+"› Ask Codex to do anything                                                      "
+"                                                                                "
+"  gpt-5.6-sol                                                ctrl + / for side  "

codex-rs/tui/src/chatwidget/snapshots/codex_tui__chatwidget__tests__side_context_label_shows_parent_status.snap

@@ -6,4 +6,4 @@ expression: terminal.backend()
 "                                                                                "
 "› Check recently modified functions for compatibility                           "
 "                                                                                "
-"  gpt-5.6-sol def… Side from main thread · main needs input · Ctrl+C to return  "
+"  Side from main thread · main needs input · ctrl + / to switch · ctrl + c to cl"

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

@@ -389,7 +389,7 @@ async fn side_context_label_preserves_status_line_snapshot() {
     chat.refresh_status_line();
     chat.set_side_conversation_active(/*active*/ true);
     chat.set_side_conversation_context_label(Some(
-        "Side from main thread · Ctrl+C to return".to_string(),
+        "Side from main thread · ctrl + / to switch · ctrl + c to close".to_string(),
     ));
 
     let width = 80;
@@ -410,7 +410,8 @@ async fn side_context_label_shows_parent_status_snapshot() {
     chat.show_welcome_banner = false;
     chat.set_side_conversation_active(/*active*/ true);
     chat.set_side_conversation_context_label(Some(
-        "Side from main thread · main needs input · Ctrl+C to return".to_string(),
+        "Side from main thread · main needs input · ctrl + / to switch · ctrl + c to close"
+            .to_string(),
     ));
 
     let width = 80;
@@ -421,3 +422,27 @@ async fn side_context_label_shows_parent_status_snapshot() {
         .expect("draw side conversation footer");
     assert_chatwidget_snapshot!("side_context_label_shows_parent_status", terminal.backend());
 }
+
+#[tokio::test]
+async fn side_context_label_shows_hidden_side_snapshot() {
+    let (mut chat, _rx, _op_rx) = make_chatwidget_manual(/*model_override*/ None).await;
+    chat.show_welcome_banner = false;
+    chat.config.tui_status_line = Some(vec!["model-name".to_string()]);
+    chat.refresh_status_line();
+    chat.set_side_conversation_context_label(Some("ctrl + / for side".to_string()));
+
+    let width = 80;
+    let height = chat.desired_height(width);
+    let mut terminal = Terminal::new(TestBackend::new(width, height)).expect("create terminal");
+    terminal
+        .draw(|f| chat.render(f.area(), f.buffer_mut()))
+        .expect("draw hidden side conversation footer");
+    let hint_start = width - "ctrl + / for side".len() as u16 - 2;
+    assert_eq!(
+        terminal.backend().buffer()[(hint_start, height - 1)]
+            .style()
+            .fg,
+        Some(ratatui::style::Color::Magenta)
+    );
+    assert_chatwidget_snapshot!("side_context_label_shows_hidden_side", terminal.backend());
+}