Support the Responses API for OpenAI API compatible

[letanloc1998]

Before submitting your bug report

• I've tried using the "Ask AI" feature on the Continue docs site to see if the docs have an answer
• I believe this is a bug. I'll try to join the Continue Discord for questions
• I'm not able to find an open issue that reports the same bug
• I've seen the troubleshooting guide on the Continue Docs

Relevant environment info

Description

Hi,

I cannot using Cloudflare models because of responses endpoint (/v1/responses)

From Open AI documentation

https://platform.openai.com/docs/guides/migrate-to-responses

Migrate to the Responses API

The Responses API is our new API primitive, an evolution of Chat Completions which brings added simplicity and powerful agentic primitives to your integrations.

While Chat Completions remains supported, Responses is recommended for all new projects.

Config

Currently, new models from Cloudflare only support response API (Eg: https://developers.cloudflare.com/workers-ai/models/gpt-oss-120b/)

How to config to use the responses endpoint?

I only found the document to use chat/completions instead of completions
https://docs.continue.dev/customize/model-providers/top-level/openai#how-to-force-legacy-completions-endpoint-usage

To reproduce

No response

Log output

[RomneyDa]

@letanloc1998 there is a PR to add support for some models through /responses, should be in soon!
#7891

[letanloc1998]

@letanloc1998 there is a PR to add support for some models through /responses, should be in soon! #7891

Great, hope it comes soon