Add support for a separate chatgpt auth endpoint (#1712)

Adds a `CodexAuth` type that encapsulates information about available
auth modes and logic for refreshing the token.
Changes `Responses` API to send requests to different endpoints based on
the auth type.
Updates login_with_chatgpt to support API-less mode and skip the key
exchange.

codex-rs/core/tests/live_agent.rs

@@ -50,7 +50,7 @@ async fn spawn_codex() -> Result<Codex, CodexErr> {
     config.model_provider.request_max_retries = Some(2);
     config.model_provider.stream_max_retries = Some(2);
     let CodexSpawnOk { codex: agent, .. } =
-        Codex::spawn(config, std::sync::Arc::new(Notify::new())).await?;
+        Codex::spawn(config, None, std::sync::Arc::new(Notify::new())).await?;
 
     Ok(agent)
 }