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/config.rs

@@ -526,6 +526,7 @@ impl Config {
                 .chatgpt_base_url
                 .or(cfg.chatgpt_base_url)
                 .unwrap_or("https://chatgpt.com/backend-api/".to_string()),
+
             experimental_resume,
             include_plan_tool: include_plan_tool.unwrap_or(false),
         };
@@ -794,7 +795,7 @@ disable_response_storage = true
 
         let openai_chat_completions_provider = ModelProviderInfo {
             name: "OpenAI using Chat Completions".to_string(),
-            base_url: "https://api.openai.com/v1".to_string(),
+            base_url: Some("https://api.openai.com/v1".to_string()),
             env_key: Some("OPENAI_API_KEY".to_string()),
             wire_api: crate::WireApi::Chat,
             env_key_instructions: None,
@@ -804,6 +805,7 @@ disable_response_storage = true
             request_max_retries: Some(4),
             stream_max_retries: Some(10),
             stream_idle_timeout_ms: Some(300_000),
+            requires_auth: false,
         };
         let model_provider_map = {
             let mut model_provider_map = built_in_model_providers();