app-server: centralize AuthManager initialization (#16764)

Extract a shared helper that builds AuthManager from Config and applies
the forced ChatGPT workspace override in one place.

Create the shared AuthManager at MessageProcessor call sites so that
upcoming new transport's initialization can reuse the same handle, and
keep only external auth refresher wiring inside `MessageProcessor`.

Remove the now-unused `AuthManager::shared_with_external_auth` helper.

codex-rs/app-server/src/message_processor/tracing_tests.rs

@@ -27,6 +27,7 @@ use codex_core::config_loader::CloudRequirementsLoader;
 use codex_core::config_loader::LoaderOverrides;
 use codex_exec_server::EnvironmentManager;
 use codex_feedback::CodexFeedback;
+use codex_login::AuthManager;
 use codex_protocol::protocol::SessionSource;
 use codex_protocol::protocol::W3cTraceContext;
 use opentelemetry::global;
@@ -234,6 +235,8 @@ fn build_test_processor(
 ) {
     let (outgoing_tx, outgoing_rx) = mpsc::channel(16);
     let outgoing = Arc::new(OutgoingMessageSender::new(outgoing_tx));
+    let auth_manager =
+        AuthManager::shared_from_config(config.as_ref(), /*enable_codex_api_key_env*/ false);
     let processor = MessageProcessor::new(MessageProcessorArgs {
         outgoing,
         arg0_paths: Arg0DispatchPaths::default(),
@@ -246,7 +249,7 @@ fn build_test_processor(
         log_db: None,
         config_warnings: Vec::new(),
         session_source: SessionSource::VSCode,
-        enable_codex_api_key_env: false,
+        auth_manager,
         rpc_transport: AppServerRpcTransport::Stdio,
     });
     (processor, outgoing_rx)