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/src/codex_wrapper.rs

@@ -6,6 +6,7 @@ use crate::config::Config;
 use crate::protocol::Event;
 use crate::protocol::EventMsg;
 use crate::util::notify_on_sigint;
+use codex_login::load_auth;
 use tokio::sync::Notify;
 use uuid::Uuid;
 
@@ -25,11 +26,12 @@ pub struct CodexConversation {
 /// that callers can surface the information to the UI.
 pub async fn init_codex(config: Config) -> anyhow::Result<CodexConversation> {
     let ctrl_c = notify_on_sigint();
+    let auth = load_auth(&config.codex_home)?;
     let CodexSpawnOk {
         codex,
         init_id,
         session_id,
-    } = Codex::spawn(config, ctrl_c.clone()).await?;
+    } = Codex::spawn(config, auth, ctrl_c.clone()).await?;
 
     // The first event must be `SessionInitialized`. Validate and forward it to
     // the caller so that they can display it in the conversation history.