fix(auth): isolate chatgptAuthTokens concept to auth manager and app-server (#10423)

So that the rest of the codebase (like TUI) don't need to be concerned
whether ChatGPT auth was handled by Codex itself or passed in via
app-server's external auth mode.

codex-rs/core/tests/suite/client_websockets.rs

@@ -14,6 +14,7 @@ use codex_core::features::Feature;
 use codex_core::models_manager::manager::ModelsManager;
 use codex_core::protocol::SessionSource;
 use codex_otel::OtelManager;
+use codex_otel::TelemetryAuthMode;
 use codex_otel::metrics::MetricsClient;
 use codex_otel::metrics::MetricsConfig;
 use codex_protocol::ThreadId;
@@ -446,7 +447,7 @@ async fn websocket_harness_with_runtime_metrics(
         model_info.slug.as_str(),
         None,
         Some("test@test.com".to_string()),
-        auth_manager.get_auth_mode(),
+        auth_manager.auth_mode().map(TelemetryAuthMode::from),
         false,
         "test".to_string(),
         SessionSource::Exec,