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>

libs/service/src/hooks/winners/index.ts

@@ -1,13 +1,11 @@
 import { useQuery } from '@tanstack/react-query';
 import { hackathonApi, HackathonApiResponse } from '../../api/hackathon';
 
-// Query keys
 export const winnerKeys = {
   all: ['winners'] as const,
   lists: () => [...winnerKeys.all, 'list'] as const,
 };
 
-// API response types
 interface Team {
   id: string;
   name: string;