Clean up frontend: compact model select + polished UI

まず src/components/chat/model-selector.tsx と現在のモデル状態の流れを読み、次に src/components/providers.tsx と src/components/chat/chat-panel.tsx を確認します。共有の ModelProvider を追加し、セレクターを src/components/nav.tsx に移動し、Claude と Gemini の SVG アイコンを src/components/icons/model-icons.tsx に作成します。コンパクトな nav セレクターでチャットモデルを制御でき、枠線付きのセレクターヘッダーが削除されていれば完了です。

Why

The current model selector uses two large side-by-side cards that take up too much vertical space and don't feel polished enough for the hackathon demo. We want to impress judges with a minimal, clean interface.

What

• Replace card-based model selector with a compact Select dropdown in the nav bar
• Add proper Claude and Gemini icon marks (SVG, icon-only — no text logos)
• Remove the bordered header section from the chat panel — the selector moves into the nav
• Create a shared model context so nav and chat panel can share model state cleanly

Files to touch

Reference

Style/font inspiration: https://github.com/lfglabs-dev/private-ethereum-assistant