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/client.rs

@@ -623,7 +623,7 @@ mod tests {
             request_max_retries: Some(0),
             stream_max_retries: Some(0),
             stream_idle_timeout_ms: Some(1000),
-            requires_auth: false,
+            requires_openai_auth: false,
         };
 
         let events = collect_events(
@@ -683,7 +683,7 @@ mod tests {
             request_max_retries: Some(0),
             stream_max_retries: Some(0),
             stream_idle_timeout_ms: Some(1000),
-            requires_auth: false,
+            requires_openai_auth: false,
         };
 
         let events = collect_events(&[sse1.as_bytes()], provider).await;
@@ -786,7 +786,7 @@ mod tests {
                 request_max_retries: Some(0),
                 stream_max_retries: Some(0),
                 stream_idle_timeout_ms: Some(1000),
-                requires_auth: false,
+                requires_openai_auth: false,
             };
 
             let out = run_sse(evs, provider).await;