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/login/Cargo.toml

@@ -24,7 +24,6 @@ http = { workspace = true }
 once_cell = { workspace = true }
 os_info = { workspace = true }
 rand = { workspace = true }
-reqwest = { workspace = true, features = ["json", "blocking"] }
 serde = { workspace = true, features = ["derive"] }
 serde_json = { workspace = true }
 sha2 = { workspace = true }