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.

app.config.ts

@@ -0,0 +1,24 @@
+export default defineAppConfig({
+  ui: {
+    primary: 'sky',
+    gray: 'slate',
+    notifications: {
+      position: 'bottom-right'
+    },
+    button: {
+      default: {
+        color: 'neutral'
+      }
+    },
+    card: {
+      default: {
+        header: {
+          padding: 'px-4 py-3'
+        },
+        body: {
+          padding: 'px-4 py-4'
+        }
+      }
+    }
+  }
+})