[Chrome extension] Modernize Complete UI Shell as per new UX #49

Task Summary
Implement the foundational UI components and state management system for the new extension, ensuring a clean and modern design. This task will provide a stable base for integrating all V1 and V2 features.

Implementation Notes

Utilize a modern front-end framework (React) to build the UI.

Establish a global state management solution (e.g., Redux, Zustand) to handle data flows between the background script and the popup/devtools panel.

Create initial placeholder components for the main dashboard, settings, and profile viewer.

Set up CSS-in-JS or a similar styling solution for maintaining consistent branding.

Checklist

• Improve the project with the chosen framework and a build system (e.g., Webpack, Vite).
• Implement the core UI layout and navigation structure.
• Set up a centralized state management store.
• Define and implement the component library for the new UI.
• Ensure the extension's manifest file is configured for V2 standards.