feat(ui): overhaul interface with Nuxt UI

Integrate the Nuxt UI component library and completely revamp the application's user interface to improve usability, aesthetics, and maintainability.

- Replace all custom components and native browser dialogs (`alert`, `prompt`, `confirm`) with Nuxt UI components like `UCard`, `UButton`, `UModal`, and `UNotifications`.
- Refactor the main page by extracting the sidebar into dedicated panel components: `CategoryPanel`, `BoardSummaryPanel`, and `HistoryPanel`.
- Redesign all major components (Toolbar, Board, Stage, Task) for a cleaner layout and improved information hierarchy.
- Implement user-friendly modals for all creation, editing, and deletion flows, providing a more consistent user experience.
- Add toast notifications to provide immediate feedback for user actions.

package.json

@@ -22,7 +22,8 @@
     "tailwindcss": "^3.4.13",
     "postcss": "^8.4.47",
     "autoprefixer": "^10.4.19",
-    "@types/node": "^20.11.30"
+    "@types/node": "^20.11.30",
+    "@nuxt/ui": "^2.15.1",
+    "@nuxt/icon": "^1.5.0"
   }
 }
-