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/deny.toml

@@ -244,7 +244,6 @@ deny = [
         "codex-core",
         "codex-exec-server",
         "codex-lmstudio",
-        "codex-login",
         "codex-ollama",
         "codex-otel",
         "codex-protocol",