Add Daybreak state to the status line and terminal title (#49861)

## What changed

Add a selectable `daybreak` item to the status line and terminal title, including setup previews and terminal-title validation. Display `Daybreak on` when enabled for the thread and `Daybreak off` otherwise, including during side conversations.

## Testing

Add coverage for on/off rendering and side conversations, update setup preview snapshots, and verify that terminal-title diagnostics accept `daybreak`.

GitOrigin-RevId: b0b7a6f0ee0a107ba4ee2d56113a5b9b6ebd1d41

codex-rs/cli/src/doctor/title.rs

@@ -142,6 +142,7 @@ fn terminal_title_item_id(item: &str) -> Option<&'static str> {
         "total-output-tokens" => Some("total-output-tokens"),
         "thread-id" | "session-id" => Some("thread-id"),
         "fast-mode" => Some("fast-mode"),
+        "daybreak" => Some("daybreak"),
         "model" | "model-name" => Some("model"),
         "model-with-reasoning" => Some("model-with-reasoning"),
         "reasoning" => Some("reasoning"),
@@ -309,11 +310,12 @@ mod tests {
     }
 
     #[test]
-    fn terminal_title_accepts_thread_usage_items() {
+    fn terminal_title_accepts_configured_items() {
         let check = terminal_title_check_from_inputs(TerminalTitleInputs {
             configured_items: Some(vec![
                 "thread-credits".to_string(),
                 "estimated-thread-cost".to_string(),
+                "daybreak".to_string(),
             ]),
             cwd: PathBuf::from("/workspace/project"),
             project_root: None,
@@ -321,11 +323,9 @@ mod tests {
 
         assert_eq!(check.status, CheckStatus::Ok);
         assert_eq!(check.summary, "terminal title configured");
-        assert!(
-            check.details.contains(
-                &"terminal title items: thread-credits, estimated-thread-cost".to_string()
-            )
-        );
+        assert!(check.details.contains(
+            &"terminal title items: thread-credits, estimated-thread-cost, daybreak".to_string()
+        ));
         assert!(check.issues.is_empty());
     }