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.rs

@@ -21,6 +21,7 @@ use codex_core::protocol::EventMsg;
 use codex_core::protocol::Op;
 use codex_core::protocol::SessionSource;
 use codex_otel::OtelManager;
+use codex_otel::TelemetryAuthMode;
 use codex_protocol::ThreadId;
 use codex_protocol::config_types::CollaborationMode;
 use codex_protocol::config_types::ModeKind;
@@ -1257,7 +1258,7 @@ async fn azure_responses_request_includes_store_and_reasoning_ids() {
         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,