Cursor Chat Completions

Cursor-specific endpoint that accepts Responses API input format but returns chat completions format.

This endpoint handles requests from Cursor IDE which sends Responses API format (input field) but expects chat completions format response (choices, messages, etc.).

curl -X POST http://localhost:4000/cursor/chat/completions     -H "Content-Type: application/json"     -H "Authorization: Bearer sk-1234"     -d '{
    "model": "gpt-4o",
    "input": [{"role": "user", "content": "Hello"}]
}'
Responds back in chat completions format.