TanStack/router ? reverse-engineered prompt

Build me a small but polished web app using TanStack Router, and if it makes sense, TanStack Start for the full stack part.

I want it to feel like a real production app, with a home page, a list page, and a detail page that uses typed route params and search params. Add nested layouts, a loading state, and a friendly error page. On the list page, let me filter and sort with the URL so the state stays shareable and back button friendly. Prefetch data when hovering links if that fits naturally, and make navigation feel snappy.

If you need to check current docs online while building it, go ahead. Keep the code clean and easy to follow, and make sure the app shows off the main strengths of the router, especially type safety, route based data loading, and SSR if you use Start.