[ENHANCEMENT] Add a model selector to the chat input area

[daewoongoh]

Problem (one or two sentences)

The chat input area only had an API configuration (profile) selector, so users had to leave the chat and go into Settings to change the actual model — even though switching models is a very common action.

Context (who is affected and when)

This affects anyone chatting who wants to quickly try a different model mid-conversation. Currently they have to interrupt their workflow, open Settings, find the relevant provider, and change the model there before returning to chat.

Desired behavior (conceptual, not technical)

Add a model selector directly in the chat input toolbar, next to the existing mode/API-config selectors, so users can switch models inline without leaving the chat.

Constraints / preferences (optional)

• Should support both dynamic-model providers (e.g., OpenRouter) and static-model providers.
• Should be searchable when the model list is long.
• Should degrade gracefully for providers where inline model selection isn't supported (e.g., show a tooltip pointing back to Settings) instead of breaking or hiding the control entirely.
• Needs i18n coverage across all supported locales.

Request checklist

• I've searched existing Issues and Discussions for duplicates
• This describes a specific problem with clear context and impact

Zoo Code Task Links (optional)

No response

Acceptance criteria (optional)

No response

Proposed approach (optional)

Add a ModelSelector component reusing useRouterModels/getStaticModelsForProvider to source the model list per provider, and mount it in ChatTextArea alongside the other selectors. Add selectModel / selectModelUnsupported strings to chat.json in every locale.

Trade-offs / risks (optional)

No response