Set codex SDK TypeScript originator (#4894)

## Summary
- ensure the TypeScript SDK sets CODEX_INTERNAL_ORIGINATOR_OVERRIDE to
codex_sdk_ts when spawning the Codex CLI
- extend the responses proxy test helper to capture request headers for
assertions
- add coverage that verifies Codex threads launched from the TypeScript
SDK send the codex_sdk_ts originator header

## Testing
- Not Run (not requested)


------
https://chatgpt.com/codex/tasks/task_i_68e561b125248320a487f129093d16e7

codex-rs/exec/tests/suite/mod.rs

@@ -1,6 +1,7 @@
 // Aggregates all former standalone integration tests as modules.
 mod apply_patch;
 mod auth_env;
+mod originator;
 mod output_schema;
 mod resume;
 mod sandbox;