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/package.json

@@ -14,8 +14,12 @@
     "@react-three/fiber": "^9.4.0",
     "@tanstack/react-query": "^5.90.10",
     "@types/react-plotly.js": "^2.6.3",
+    "@types/react-syntax-highlighter": "^15.5.13",
     "@types/three": "^0.181.0",
+    "@xterm/addon-fit": "^0.10.0",
+    "@xterm/addon-web-links": "^0.11.0",
     "clsx": "^2.1.1",
+    "katex": "^0.16.25",
     "lucide-react": "^0.554.0",
     "plotly.js-basic-dist": "^3.3.0",
     "react": "^18.2.0",
@@ -23,13 +27,15 @@
     "react-markdown": "^10.1.0",
     "react-plotly.js": "^2.6.0",
     "react-router-dom": "^6.20.0",
+    "react-syntax-highlighter": "^16.1.0",
     "react-use-websocket": "^4.13.0",
     "recharts": "^2.10.3",
     "rehype-katex": "^7.0.1",
     "remark-gfm": "^4.0.1",
     "remark-math": "^6.0.0",
     "tailwind-merge": "^3.4.0",
-    "three": "^0.181.2"
+    "three": "^0.181.2",
+    "xterm": "^5.3.0"
   },
   "devDependencies": {
     "@types/react": "^18.2.43",