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.rs

@@ -15,6 +15,7 @@ use async_channel::Sender;
 use codex_apply_patch::ApplyPatchAction;
 use codex_apply_patch::MaybeApplyPatchVerified;
 use codex_apply_patch::maybe_parse_apply_patch_verified;
+use codex_login::CodexAuth;
 use futures::prelude::*;
 use mcp_types::CallToolResult;
 use serde::Serialize;
@@ -103,7 +104,11 @@ pub struct CodexSpawnOk {
 
 impl Codex {
     /// Spawn a new [`Codex`] and initialize the session.
-    pub async fn spawn(config: Config, ctrl_c: Arc<Notify>) -> CodexResult<CodexSpawnOk> {
+    pub async fn spawn(
+        config: Config,
+        auth: Option<CodexAuth>,
+        ctrl_c: Arc<Notify>,
+    ) -> CodexResult<CodexSpawnOk> {
         // experimental resume path (undocumented)
         let resume_path = config.experimental_resume.clone();
         info!("resume_path: {resume_path:?}");
@@ -132,7 +137,7 @@ impl Codex {
         // Generate a unique ID for the lifetime of this Codex session.
         let session_id = Uuid::new_v4();
         tokio::spawn(submission_loop(
-            session_id, config, rx_sub, tx_event, ctrl_c,
+            session_id, config, auth, rx_sub, tx_event, ctrl_c,
         ));
         let codex = Codex {
             next_id: AtomicU64::new(0),
@@ -525,6 +530,7 @@ impl AgentTask {
 async fn submission_loop(
     mut session_id: Uuid,
     config: Arc<Config>,
+    auth: Option<CodexAuth>,
     rx_sub: Receiver<Submission>,
     tx_event: Sender<Event>,
     ctrl_c: Arc<Notify>,
@@ -636,6 +642,7 @@ async fn submission_loop(
 
                 let client = ModelClient::new(
                     config.clone(),
+                    auth.clone(),
                     provider.clone(),
                     model_reasoning_effort,
                     model_reasoning_summary,