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/utils/vite.config.ts

@@ -18,12 +18,6 @@ export default defineConfig(() => ({
       tsconfigPath: path.join(__dirname, 'tsconfig.lib.json'),
     }),
   ],
-  // Uncomment this if you are using workers.
-  // worker: {
-  //  plugins: [ nxViteTsPaths() ],
-  // },
-  // Configuration for building your library.
-  // See: https://vitejs.dev/guide/build.html#library-mode
   build: {
     outDir: '../../dist/libs/utils',
     emptyOutDir: true,
@@ -32,16 +26,12 @@ export default defineConfig(() => ({
       transformMixedEsModules: true,
     },
     lib: {
-      // Could also be a dictionary or array of multiple entry points.
       entry: 'src/index.ts',
       name: 'utils',
       fileName: 'index',
-      // Change this to the formats you want to support.
-      // Don't forget to update your package.json as well.
       formats: ['es' as const],
     },
     rollupOptions: {
-      // External packages that should not be bundled into your library.
       external: ['react', 'react-dom', 'react/jsx-runtime'],
     },
   },