After all, upgrading from Nuxt v3.10.0 to v4.0.3 fixed it.

My package.json

{
  "name": "nuxt",
  "private": true,
  "type": "module",
  "scripts": {
    "build": "nuxt build",
    "dev": "nuxt dev",
    "generate": "nuxt generate",
    "preview": "nuxt preview",
    "postinstall": "nuxt prepare"
  },
  "devDependencies": {
    "nuxt": "^4.0.3",
    "vue": "^3.4.20",
  },
  "dependencies": {
    "@pinia/nuxt": "^0.11.1",
    "pinia": "^3.0.3"
  }
}