<!-- CURSOR_SUMMARY -->
> [!NOTE]
> Introduces Responses API support for local-agent flows and aligns
OpenAI reasoning options.
> 
> - In `get_model_client.ts`, when using Dyad Pro and `selectedChatMode`
is `"local-agent"` with OpenAI, route to `provider.responses(...)`
instead of chat model
> - In `llm_engine_provider.ts`, add `responses(modelId)` returning
`OpenAIResponsesLanguageModel`, refactor request handling into
`createDyadFetch()`, and expose `provider.responses`
> - In `thinking_utils.ts`, for OpenAI in `local-agent` mode, send `{
reasoning: { summary: "detailed", effort: "medium" } }`; otherwise keep
`reasoning_effort: "medium"`
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
f434775c1c42fd9a647b5ee0e51cf5aecc7a7c8f. This will update automatically
on new commits. Configure
[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->