Prefer env var auth over default codex auth (#1861)

## Summary
- Prioritize provider-specific API keys over default Codex auth when
building requests
- Add test to ensure provider env var auth overrides default auth

## Testing
- `just fmt`
- `just fix` *(fails: `let` expressions in this position are unstable)*
- `cargo test --all-features` *(fails: `let` expressions in this
position are unstable)*

------
https://chatgpt.com/codex/tasks/task_i_68926a104f7483208f2c8fd36763e0e3

codex-rs/core/src/config.rs

@@ -842,7 +842,7 @@ disable_response_storage = true
             request_max_retries: Some(4),
             stream_max_retries: Some(10),
             stream_idle_timeout_ms: Some(300_000),
-            requires_auth: false,
+            requires_openai_auth: false,
         };
         let model_provider_map = {
             let mut model_provider_map = built_in_model_providers();