Pinia module causing [500] internal server error after upgrading to Nuxt version to 3.15.x

[s-blanar]

Reproduction

https://stackblitz.com/edit/github-6p4rt1bq

Steps to reproduce the bug

No specific steps required as when the app starts I am getting 500 internal server error.
In the console I am getting twice

[nuxt] [request error] [unhandled] [500] [🍍]: "getActivePinia()" was called but there was no active Pinia. Are you trying to use a store before calling "app.use(pinia)"?
See https://pinia.vuejs.org/core-concepts/outside-component-usage.html for help.
This will fail in production.

Expected behavior

It shouldn't produce any errors as I am using just a plain starter template with npx nuxi@latest init <my-app> and a store file from the pinia documentation example:

export const useCounterStore = defineStore("counter", () => {
    const count = ref(0)
    const name = ref("Eduardo")
    const doubleCount = computed(() => count.value * 2)
    function increment() {
        count.value++
    }

    return { count, name, doubleCount, increment }
})

and then using it in app.vue

<template>
    <div>
        <NuxtRouteAnnouncer />
        <NuxtWelcome />
    </div>
</template>
<script lang="ts">
const store = useCounterStore()
</script>

with clean nuxt.config.ts

// https://nuxt.com/docs/api/configuration/nuxt-config
export default defineNuxtConfig({
  compatibilityDate: '2024-11-01',
  devtools: { enabled: true },
  modules: ['@pinia/nuxt']
})

Actual behavior

In the console I am getting twice

[nuxt] [request error] [unhandled] [500] [🍍]: "getActivePinia()" was called but there was no active Pinia. Are you trying to use a store before calling "app.use(pinia)"?
See https://pinia.vuejs.org/core-concepts/outside-component-usage.html for help.
This will fail in production.

Additional information

The error started to show when I upgraded Nuxt version from 3.14.x to 3.15.0. I tried every new Nuxt version since, but with the same result. I tried to isolate the pinia module and created empty project from the starter template and the problem persists, so there is no module conflict. At first I thought that it is a Nuxt issue, so I created an issue in their repo (nuxt/nuxt#30751), but the Nuxt team said, it is probably a Pinia (or Pinia nuxt module) issue (nuxt/nuxt#30751 (comment)).

[posva]

You are using a regular script instead of a setup one:

<script lang="ts" setup>
const store = useCounterStore();
</script>

The issue you are falling is in the link mentioned in the warning, https://pinia.vuejs.org/core-concepts/outside-component-usage.html