Load app-server config through ConfigManager (#18870)

## Summary
- Load app-server startup config through `ConfigManager` instead of
direct `ConfigBuilder` calls.
- Move `ConfigManager` constructor-owned state (`cli_overrides`, runtime
feature map, cloud requirements loader) behind internal manager fields.
- Pass `ConfigManager` into `MessageProcessor` directly instead of
reconstructing it from raw args.

## Tests
- `cargo check -p codex-app-server`
- `cargo test -p codex-app-server`
- `just fix -p codex-app-server`
- `just fmt`

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

@@ -1,6 +1,7 @@
 use super::ConnectionSessionState;
 use super::MessageProcessor;
 use super::MessageProcessorArgs;
+use crate::config_manager::ConfigManager;
 use crate::outgoing_message::ConnectionId;
 use crate::outgoing_message::OutgoingMessageSender;
 use crate::transport::AppServerTransport;
@@ -233,15 +234,20 @@ fn build_test_processor(
     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 config_manager = ConfigManager::new(
+        config.codex_home.to_path_buf(),
+        Vec::new(),
+        LoaderOverrides::default(),
+        CloudRequirementsLoader::default(),
+        Arg0DispatchPaths::default(),
+        Arc::new(codex_config::NoopThreadConfigLoader),
+    );
     let processor = Arc::new(MessageProcessor::new(MessageProcessorArgs {
         outgoing,
         arg0_paths: Arg0DispatchPaths::default(),
         config,
+        config_manager,
         environment_manager: Arc::new(EnvironmentManager::new(/*exec_server_url*/ None)),
-        cli_overrides: Vec::new(),
-        loader_overrides: LoaderOverrides::default(),
-        cloud_requirements: CloudRequirementsLoader::default(),
-        thread_config_loader: Arc::new(codex_config::NoopThreadConfigLoader),
         feedback: CodexFeedback::new(),
         log_db: None,
         config_warnings: Vec::new(),