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/Cargo.lock

@@ -673,7 +673,9 @@ dependencies = [
  "async-channel",
  "base64 0.22.1",
  "bytes",
+ "chrono",
  "codex-apply-patch",
+ "codex-login",
  "codex-mcp-client",
  "core_test_support",
  "dirs",