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.
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