fix(tui) turn timing incremental (#9599)

## Summary
When we send multiple assistant messages, reset the timer so "Worked for
2m 36s" is the time since the last time we showed the message, rather
than an ever-increasing number.

We could instead change the copy so it's more clearly a running counter.

## Testing
- [x] ran locally

<img width="903" height="732" alt="Screenshot 2026-01-21 at 1 42 51 AM"
src="https://github.com/user-attachments/assets/bb4d827b-3a0e-48ba-bd6a-d8cd65d8e892"
/>

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

@@ -838,6 +838,7 @@ async fn make_chatwidget_manual(
         pre_review_token_info: None,
         needs_final_message_separator: false,
         had_work_activity: false,
+        last_separator_elapsed_secs: None,
         last_rendered_width: std::cell::Cell::new(None),
         feedback: codex_feedback::CodexFeedback::new(),
         current_rollout_path: None,
@@ -868,6 +869,16 @@ fn set_chatgpt_auth(chat: &mut ChatWidget) {
     ));
 }
 
+#[tokio::test]
+async fn worked_elapsed_from_resets_when_timer_restarts() {
+    let (mut chat, _rx, _op_rx) = make_chatwidget_manual(None).await;
+    assert_eq!(chat.worked_elapsed_from(5), 5);
+    assert_eq!(chat.worked_elapsed_from(9), 4);
+    // Simulate status timer resetting (e.g., status indicator recreated for a new task).
+    assert_eq!(chat.worked_elapsed_from(3), 3);
+    assert_eq!(chat.worked_elapsed_from(7), 4);
+}
+
 pub(crate) async fn make_chatwidget_manual_with_sender() -> (
     ChatWidget,
     AppEventSender,