<!-- CURSOR_SUMMARY -->
> [!NOTE]
> Fixes auto/local-agent model routing and provider-specific behavior.
> 
> - Refactors `llm_engine_provider` to require `chatParams { providerId
}`; wires it into custom fetch and model constructors (`provider`,
`chatModel`, `responses`)
> - Updates `get_model_client` to pass `providerId`, tag fallback models
(`openai`, `anthropic`, `google`), and use `responses()` for OpenAI in
`local-agent` and auto fallback
> - Adds Responses API support to fake LLM server (`/v1/responses`) with
streaming SSE handler and dump generation
> - Extends test helper to parse Responses API dumps (`body.input`) and
adds `localAgentUseAutoModel` setup flag
> - New e2e test `local_agent_auto.spec.ts` with snapshot verifying
request payload via Responses API
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
e5b02d253c9842f14da0099bb11e1b05548e9245. This will update automatically
on new commits. Configure
[here](https://cursor.com/dashboard?tab=bugbot).</sup>
<!-- /CURSOR_SUMMARY -->

<!-- This is an auto-generated description by cubic. -->
---
## Summary by cubic
Fixes auto model selection in the Dyad engine by passing the correct
providerId with each request. Ensures provider-specific options are
applied and avoids incorrect defaults.

- **Bug Fixes**
- Pass providerId to chat/responses models and into the fetch layer for
getExtraProviderOptions.
- Remove originalProviderId from createDyadEngine; add ChatParams and
update provider API signatures.
- Tag fallback models with providerId (openai, anthropic, google) and
forward model.provider in getModelClient.

<sup>Written for commit e5b02d253c9842f14da0099bb11e1b05548e9245.
Summary will update on new commits.</sup>

<!-- End of auto-generated description by cubic. -->