Feature Request: Responses API support

[spencerbart]

OpenAI has recently released the Responses API. New projects are recommended to use the Responses API over Chat Completions.

[samvrlewis]

Noticed this too so started work on it: 67d4a85

The example compiles and works but the types probably need a bit of a tidy up, some are missing documentation. WIll open a PR here in the next day or two once I clean it up but happy for any feedback in the meantime. There's some duplication of types between responses and chat that are a bit awkward as the types are nearly the same but slightly different, and as everything is exported flat from the library I needed to prepend one or two types with Responses.

[jkoppel]

Second this. The Responses API is necessary for using the codex-mini-latest model

[samvrlewis]

Opened a PR here: #373