Move auth code into login crate (#15150)

- Move the auth implementation and token data into codex-login.
- Keep codex-core re-exporting that surface from codex-login for
existing callers.

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/app-server/src/codex_message_processor.rs

@@ -191,7 +191,6 @@ use codex_core::ThreadSortKey as CoreThreadSortKey;
 use codex_core::auth::AuthMode as CoreAuthMode;
 use codex_core::auth::CLIENT_ID;
 use codex_core::auth::login_with_api_key;
-use codex_core::auth::login_with_chatgpt_auth_tokens;
 use codex_core::config::Config;
 use codex_core::config::ConfigOverrides;
 use codex_core::config::NetworkProxyAuditMetadata;
@@ -242,6 +241,7 @@ use codex_core::windows_sandbox::WindowsSandboxSetupRequest;
 use codex_feedback::CodexFeedback;
 use codex_login::ServerOptions as LoginServerOptions;
 use codex_login::ShutdownHandle;
+use codex_login::auth::login_with_chatgpt_auth_tokens;
 use codex_login::run_login_server;
 use codex_protocol::ThreadId;
 use codex_protocol::config_types::CollaborationMode;
@@ -1411,7 +1411,7 @@ impl CodexMessageProcessor {
         let account = match self.auth_manager.auth_cached() {
             Some(auth) => match auth.auth_mode() {
                 CoreAuthMode::ApiKey => Some(Account::ApiKey {}),
-                CoreAuthMode::Chatgpt => {
+                CoreAuthMode::Chatgpt | CoreAuthMode::ChatgptAuthTokens => {
                     let email = auth.get_account_email();
                     let plan_type = auth.account_plan_type();