## 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
