Migrate to HeroUI v3 and Tailwind CSS v4

- Upgrade from Tailwind CSS v3 to v4 with CSS-first configuration
- Install HeroUI v3 beta packages (@heroui/react, @heroui/styles)
- Migrate PostCSS config to new @tailwindcss/postcss plugin
- Convert tailwind.config.cjs to CSS @theme directive in globals.css
- Replace @tailwindcss/typography with custom prose styles

Component migrations:
- theme-toggle, back-to-top: HeroUI Button with onPress
- post-card, post-list-item: HeroUI Card compound components
- right-sidebar: HeroUI Card, Avatar, Chip
- search-modal: HeroUI Modal with compound structure
- nav-menu: HeroUI Button for mobile controls
- post-list-with-controls: HeroUI Button for sorting/pagination

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

package.json

@@ -17,6 +17,9 @@
   "type": "module",
   "dependencies": {
     "@emotion/is-prop-valid": "^1.4.0",
+    "@heroui/react": "^3.0.0-beta.5",
+    "@heroui/styles": "^3.0.0-beta.5",
+    "@tailwindcss/postcss": "^4.1.18",
     "@vercel/og": "^0.8.5",
     "clsx": "^2.1.1",
     "contentlayer2": "^0.5.8",
@@ -35,20 +38,19 @@
     "remark-gfm": "^4.0.1",
     "shiki": "^3.15.0",
     "tailwind-merge": "^3.4.0",
+    "tailwind-variants": "^3.2.2",
     "unist-util-visit": "^5.0.0"
   },
   "devDependencies": {
-    "@tailwindcss/typography": "^0.5.19",
     "@types/node": "^24.10.1",
     "@types/react": "^19.2.5",
     "@types/react-dom": "^19.2.3",
-    "autoprefixer": "^10.4.22",
     "concurrently": "^9.2.1",
     "eslint": "^9.39.1",
     "eslint-config-next": "^16.0.3",
     "pagefind": "^1.4.0",
     "postcss": "^8.5.6",
-    "tailwindcss": "^3.4.18",
+    "tailwindcss": "^4.1.18",
     "typescript": "^5.9.3"
   }
 }