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.

tsconfig.json

@@ -0,0 +1,7 @@
+{
+  "extends": "./.nuxt/tsconfig.json",
+  "compilerOptions": {
+    "strict": true
+  }
+}
+