[Vuejs]-Nuxt3 Layout Css is not updating when route Changes with NuxtLink

Make the styles scoped in order to be unique for each layout:

<template>
  <AppHeader />
  <slot />
</template>

<style scoped>
.header-wrapper {
  background: red;
}
</style>

and

<template>
  <AppHeader />
  <slot />
</template>

<style scoped>
.header-wrapper {
  background: blue;
}
</style>