chore: upgrade dependencies, restructure shared libs, and fix UI

- Upgrade Nx 22.1.1 → 22.6.3 and all patch/minor dependencies
- Restructure shared libs: move business logic from utils to service
- Consolidate shadcn-ui into ui lib with atomic design pattern
- Fix container centering for landing app (Tailwind v4 compatibility)
- Fix button styling by updating @source directive in globals.css
- Fix SiCss3 → SiCss rename in react-icons 5.6
- Fix duplicate useSession export conflict
- Remove dead code, comments, and unused files

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/hackathon/src/main.tsx

@@ -24,10 +24,6 @@ add404PageToRoutesChildren(notFoundFiles, routes);
 const router = createBrowserRouter([
   {
     ...routes,
-    // MIDDLEWARE TEMPORARILY DISABLED - causing infinite loops with React Router v7
-    // TODO: Implement auth checks at component level or use different pattern
-    // loader: middleware,
-    // shouldRevalidate: () => false,
   },
 ]);