refactor(app): rewrite application with Nuxt 4, Pinia, and TailwindCSS

This commit replaces the original vanilla JavaScript implementation with a modern frontend stack. The entire application has been rewritten to improve maintainability, developer experience, and leverage modern
web technologies.

Key changes include:
- Replaced plain HTML, CSS, and JS with a Nuxt 4 project structure.
- Migrated state management from a global state object to a Pinia store for better organization and reactivity.
- Rebuilt the UI with Vue 3 components and styled with TailwindCSS.
- Changed the primary persistence mechanism from manual file I/O to automatic LocalStorage saving, while retaining import/export functionality.
- All core features, including drag-and-drop, task management, and the import/merge diffing logic, have been ported to the new architecture.

utils/uuid.ts

@@ -0,0 +1,8 @@
+export function uuid() {
+  return 'xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx'.replace(/[xy]/g, c => {
+    const r = (Math.random() * 16) | 0
+    const v = c === 'x' ? r : (r & 0x3) | 0x8
+    return v.toString(16)
+  })
+}
+