Evaluate and support stream responses for both chat and responses APIs

[RulaKhaled]

https://platform.openai.com/docs/guides/streaming-responses

[linear]

JS-735 Evaluate and support stream responses for both chat and responses APIs

[github-actions]

A PR closing this issue has just been released 🚀

This issue was referenced by PR #17110, which was included in the 10.0.0 release.