Need support for `/v1/responses` endpoint

[Aneerudh2k2]

Validations

• I believe this is a way to improve. I'll try to join the Continue Discord for questions
• I'm not able to find an open issue that requests the same enhancement

Problem

Please provide support for openai compatible endpoints like /v1/responses because certain models only compatible with this endpoint

Solution

include support for /v1/responses

[sestinj]

Marking as good-first-issue. The initial change to make here would be adding support in OpenAI.ts