feat: replace carousel using alpine with javascript

package.json

@@ -11,7 +11,6 @@
     "format:write": "prettier --write ."
   },
   "dependencies": {
-    "@astrojs/alpinejs": "^0.4.3",
     "@astrojs/check": "0.9.4",
     "@astrojs/mdx": "^4.0.8",
     "@astrojs/rss": "^4.0.11",
@@ -20,8 +19,6 @@
     "@fontsource-variable/red-hat-mono": "^5.1.1",
     "@fontsource/instrument-serif": "^5.1.1",
     "@tailwindcss/vite": "^4.0.6",
-    "@types/alpinejs": "^3.13.11",
-    "alpinejs": "^3.14.8",
     "astro": "^5.3.0",
     "astro-icon": "^1.1.5",
     "rehype-external-links": "^3.0.0",