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/config_api.rs

@@ -432,7 +432,6 @@ mod tests {
     use pretty_assertions::assert_eq;
     use serde_json::json;
     use std::collections::BTreeMap;
-    use std::sync::RwLock;
     use std::sync::atomic::AtomicUsize;
     use std::sync::atomic::Ordering;
     use tempfile::TempDir;
@@ -733,10 +732,9 @@ mod tests {
         let config_api = ConfigApi::new(
             ConfigManager::new(
                 codex_home.path().to_path_buf(),
-                Arc::new(RwLock::new(Vec::new())),
-                Arc::new(RwLock::new(BTreeMap::new())),
+                Vec::new(),
                 LoaderOverrides::default(),
-                Arc::new(RwLock::new(CloudRequirementsLoader::default())),
+                CloudRequirementsLoader::default(),
                 Arg0DispatchPaths::default(),
                 Arc::new(codex_config::NoopThreadConfigLoader),
             ),