nuxtpage: child page inside parent page

//layouts/default.vue
<template>
  <div>
      <slot />
  </div>
</template>

//app.vue
<template>
  <div>
    <NuxtLayout>
      <NuxtPage />
    </NuxtLayout>
  </div>
</template>

//categories/index.vue
<template>
  <div class="flex">
    <div class="w-full">
      Categories
      <uLink to="/categories/cat1">Cat1</uLink>
      <uLink to="/categories/cat2">Cat2</uLink>
      <uLink to="/categories/cat3">Cat3</uLink>
    </div>
    <div>
      <NuxtPage :page-key="(route) => route.fullPath" />
    </div>
  </div>
</template>

//categories/[category].vue
<script setup>
  const { category } = useRoute().params;
</script>
<template>
  <div class="w-full">Sub Assortment {{ category }}</div>
</template>