<!-- CURSOR_SUMMARY -->
> [!NOTE]
> Improves local-agent auto mode with robust model routing and updates
tests accordingly.
> 
> - Centralizes pro model selection in `getProModelClient`, routing
OpenAI via `responses` in local-agent and adding local fallback across
`GPT_5.2`, `Claude Sonnet 4.5`, and `Gemini 3 Flash`
> - Standardizes model IDs via constants and updates provider/thinking
flags (adds reasoning for `auto` provider)
> - e2e: introduce `clickRunSecurityReview()` helper; select Anthropic
model in local-agent; refresh snapshots to use `reasoning_effort` and
reflect non-OpenAI model
> 
> <sup>Written by [Cursor
Bugbot](https://cursor.com/dashboard?tab=bugbot) for commit
b3fd078d2b893ebc6d011365295948a17ea58c4f. 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
Enables reliable local-agent auto mode with smart model fallback and
routes OpenAI models through Responses to keep reasoning features
working. Standardizes model names with constants.

- **New Features**
- Auto mode falls back across GPT‑5.2 (OpenAI), Claude Sonnet 4.5
(Anthropic), and Gemini 3 Flash (Google).
- OpenAI models use the Responses API to support thinking summaries and
full functionality.
  - Auto provider enables reasoning options in local-agent.

- **Refactors**
- Centralized pro model routing in getProModelClient and avoids free
variants.
- Added constants for model IDs (GPT_5_2_MODEL_NAME, SONNET_4_5,
GEMINI_3_FLASH).

<sup>Written for commit b3fd078d2b893ebc6d011365295948a17ea58c4f.
Summary will update on new commits.</sup>

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