Do not poll for usage when using API Key auth (#10973)

Fixes #10869

- Gate TUI rate-limit polling on ChatGPT-auth providers only.
- `prefetch_rate_limits()` now checks `should_prefetch_rate_limits()`.
- New gate requires:
  - `config.model_provider.requires_openai_auth`
  - cached auth is ChatGPT (`CodexAuth::is_chatgpt_auth`)
- Prevents `/wham/usage` polling in API/custom-endpoint profiles.

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

@@ -1138,6 +1138,22 @@ fn set_chatgpt_auth(chat: &mut ChatWidget) {
     ));
 }
 
+#[tokio::test]
+async fn prefetch_rate_limits_is_gated_on_chatgpt_auth_provider() {
+    let (mut chat, _rx, _op_rx) = make_chatwidget_manual(None).await;
+
+    assert!(!chat.should_prefetch_rate_limits());
+
+    set_chatgpt_auth(&mut chat);
+    assert!(chat.should_prefetch_rate_limits());
+
+    chat.config.model_provider.requires_openai_auth = false;
+    assert!(!chat.should_prefetch_rate_limits());
+
+    chat.prefetch_rate_limits();
+    assert!(chat.rate_limit_poller.is_none());
+}
+
 #[tokio::test]
 async fn worked_elapsed_from_resets_when_timer_restarts() {
     let (mut chat, _rx, _op_rx) = make_chatwidget_manual(None).await;