#7677: feat(ui): add model selection and reasoning level control to WebChat

This PR introduces two highly requested features to the WebChat interface: 1. Model Selector: Users can now dynamically switch between available primary models directly from the chat compose area without changing the global configuration. 2. Reasoning Level Toggle: Added a selector for reasoningLevel (Off, On, Stream). This is particularly useful for models with long thinking chains (like Claude 4.5), and also fixes issues where Gemini models' responses were hidden due to default reasoning settings. 3. Session Persistence: UI choices are patched back to the session state on the gateway, ensuring consistency across reloads.