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/landing/src/app/(public)/(home)/_components/cta-section.tsx

@@ -11,7 +11,7 @@ export function CTASection() {
 
   return (
     <section className="w-full py-20 md:py-32 bg-gradient-to-br from-primary-500 to-primary-600 relative overflow-hidden">
-      {/* Background pattern */}
+
       <div
         className="absolute inset-0 opacity-10"
         style={{
@@ -21,7 +21,7 @@ export function CTASection() {
 
       <div className="container relative" ref={ref}>
         <div className="flex flex-col lg:flex-row items-center justify-between gap-12">
-          {/* Text Content */}
+
           <div className="flex-1 text-center lg:text-left space-y-8">
             <motion.div
               initial={{ opacity: 0, y: 30 }}
@@ -65,7 +65,6 @@ export function CTASection() {
             </motion.div>
           </div>
 
-          {/* Illustration */}
           <motion.div
             initial={{ opacity: 0, x: 50 }}
             animate={isInView ? { opacity: 1, x: 0 } : {}}