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/backend-client/src/client/rate_limit_resets.rs

@@ -7,8 +7,9 @@ use crate::types::RateLimitResetCreditsDetails;
 use crate::types::RateLimitStatusWithResetCredits;
 use crate::types::RateLimitsWithResetCredits;
 use anyhow::Result;
-use reqwest::header::CONTENT_TYPE;
-use reqwest::header::HeaderValue;
+use http::Method;
+use http::header::CONTENT_TYPE;
+use http::header::HeaderValue;
 use serde::Serialize;
 
 #[derive(Serialize)]
@@ -29,14 +30,14 @@ impl Client {
 
     pub(super) async fn get_rate_limit_status(&self) -> Result<RateLimitStatusWithResetCredits> {
         let url = self.rate_limit_status_url();
-        let req = self.http.get(&url).headers(self.headers());
+        let req = self.request(Method::GET, &url).headers(self.headers());
         let (body, ct) = self.exec_request(req, "GET", &url).await?;
         self.decode_json(&url, &ct, &body)
     }
 
     pub async fn list_rate_limit_reset_credits(&self) -> Result<RateLimitResetCreditsDetails> {
         let url = self.rate_limit_reset_credits_url();
-        let req = self.http.get(&url).headers(self.headers());
+        let req = self.request(Method::GET, &url).headers(self.headers());
         let (body, ct) = self.exec_request(req, "GET", &url).await?;
         self.decode_json(&url, &ct, &body)
     }
@@ -65,8 +66,7 @@ impl Client {
     ) -> Result<ConsumeRateLimitResetCreditResponse> {
         let url = self.consume_rate_limit_reset_credit_url();
         let req = self
-            .http
-            .post(&url)
+            .request(Method::POST, &url)
             .headers(self.headers())
             .header(CONTENT_TYPE, HeaderValue::from_static("application/json"))
             .json(&ConsumeRateLimitResetCreditRequest {

codex-rs/backend-client/src/client/rate_limit_resets_tests.rs

@@ -138,7 +138,12 @@ fn rate_limit_reset_contract_uses_expected_paths_and_payloads() {
 fn test_client(base_url: &str, path_style: PathStyle) -> Client {
     Client {
         base_url: base_url.to_string(),
-        http: reqwest::Client::new(),
+        http: codex_http_client::RouteAwareClientPool::new(
+            codex_http_client::HttpClientFactory::new(
+                codex_http_client::OutboundProxyPolicy::ReqwestDefault,
+            ),
+            codex_http_client::ClientRouteClass::Api,
+        ),
         auth_provider: codex_model_provider::unauthenticated_auth_provider(),
         user_agent: None,
         chatgpt_account_id: None,