Route backend requests through the HTTP client factory (#34490)

## Why

Backend-backed features need to use the same outbound routing configuration as the rest of Codex.

## What changed

- Build the backend client on a route-aware client pool supplied by `HttpClientFactory`.
- Pass the configured factory through app-server account requests, cloud config loading, cloud tasks, and memory rate-limit checks.
- Preserve task query encoding, authentication headers, JSON request bodies, and ChatGPT cookie handling during the migration.

## Testing

- Add backend-client tests for proxy-policy propagation, task query encoding, bearer authentication, and JSON request bodies.

GitOrigin-RevId: c17d162e0dce9cec758df7cdeecf982207c6512b

codex-rs/cloud-tasks/src/lib.rs

@@ -60,7 +60,9 @@ async fn init_backend(user_agent_suffix: &str) -> anyhow::Result<BackendContext>
     }
 
     let ua = get_codex_user_agent();
-    let mut http = codex_cloud_tasks_client::HttpClient::new(base_url.clone())?.with_user_agent(ua);
+    let (auth_manager, http_client_factory) = util::load_auth_manager(Some(base_url.clone())).await;
+    let mut http = codex_cloud_tasks_client::HttpClient::new(base_url.clone(), http_client_factory)
+        .with_user_agent(ua);
     let style = if base_url.contains("/backend-api") {
         "wham"
     } else {
@@ -68,7 +70,6 @@ async fn init_backend(user_agent_suffix: &str) -> anyhow::Result<BackendContext>
     };
     append_error_log(format!("startup: base_url={base_url} path_style={style}"));
 
-    let auth_manager = util::load_auth_manager(Some(base_url.clone())).await;
     let auth = match auth_manager.as_ref() {
         Some(manager) => manager.auth().await,
         None => None,