feat: Add Claude Code terminal integration to dashboard

- Add embedded Claude Code terminal with xterm.js for full CLI experience
- Create WebSocket PTY backend for real-time terminal communication
- Add terminal status endpoint to check CLI availability
- Update dashboard to use Claude Code terminal instead of API chat
- Add optimization control panel with start/stop/validate actions
- Add study context provider for global state management
- Update frontend with new dependencies (xterm.js addons)
- Comprehensive README documentation for all new features

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

atomizer-dashboard/frontend/src/index.css

@@ -1,3 +1,5 @@
+@import 'katex/dist/katex.min.css';
+
 @tailwind base;
 @tailwind components;
 @tailwind utilities;