## Why
Standalone web search selected a proxy route only for the initial endpoint. Redirect destinations can require a different system proxy route.
## What changed
- Add `RouteAwareClientPool` support to `ReqwestTransport` for both buffered and streaming requests, and use it for standalone web search.
- Preserve default Codex headers and Cloudflare cookie handling across routes, while retaining the default client behavior when route-aware handling is disabled or Codex is sandboxed.
- Share request construction so URL authentication and header precedence follow `reqwest` semantics, applying them once before redirects and TLS retries.
- Map route-aware failures to transport errors and remove request URLs from those errors.
## Testing
Add regression coverage for redirects through distinct proxies, preservation of POST bodies and default headers, URL authentication and header precedence, and transport error classification without URL leakage.
GitOrigin-RevId: 19a10a62118846db09dd95265dc277e54aac09ef
Celia Chen
6ea62c4396