Migrate login HTTP construction to HttpClient (#34643)

## Why

`codex-http-client` is the intended owner of direct `reqwest` usage.

## What changed

- Build Codex's default and route-aware clients with `HttpClientBuilder`, and return `HttpClient` directly to API, model discovery, auth, remote control, skills, and extension callers.
- Preserve custom CA, proxy, Cloudflare cookie, sandbox, and request-logging policies while removing `codex-login`'s direct `reqwest` dependency.
- Use shared HTTP types for auth headers, status codes, transport errors, and login-server tests.

## Testing

- Add a Linux integration test verifying that a regular Responses API turn traverses the configured system proxy.

GitOrigin-RevId: 714695fb80762d2083e2f7a6414183e2b3b63854

codex-rs/core-skills/src/remote.rs

@@ -7,7 +7,7 @@ use std::path::PathBuf;
 use std::time::Duration;
 
 use codex_login::CodexAuth;
-use codex_login::default_client::build_reqwest_client;
+use codex_login::default_client::create_client_without_request_logging;
 
 const REMOTE_SKILLS_API_TIMEOUT: Duration = Duration::from_secs(30);
 
@@ -107,7 +107,7 @@ pub async fn list_remote_skills(
         query_params.push(("enabled", enabled));
     }
 
-    let client = build_reqwest_client();
+    let client = create_client_without_request_logging();
     let request = client
         .get(&url)
         .timeout(REMOTE_SKILLS_API_TIMEOUT)
@@ -146,7 +146,7 @@ pub async fn export_remote_skill(
 ) -> Result<RemoteSkillDownloadResult> {
     let auth = ensure_codex_backend_auth(auth)?;
 
-    let client = build_reqwest_client();
+    let client = create_client_without_request_logging();
     let base_url = chatgpt_base_url.trim_end_matches('/');
     let url = format!("{base_url}/hazelnuts/{skill_id}/export");
     let request = client