我认为错误出现在应用程序的入口点的以下行中：

app.use(createPinia()); // this is using one instance of pinia
const pinia = createPinia() // here you are creating a second instance of pinia
pinia.use(piniaPluginPersistedstate) // here you are applying a package to the second instance that is not the one which is connected to the vue app.

你能试试这个吗

app.use(pinia) // after the pinia.use declaration

检查PPS的导入语句和使用情况
并在import语句中使用良好的顺序：

import { createApp} from "vue";
import { createPinia } from "pinia";
import piniaPluginPersistedstate from 'pinia-plugin-persistedstate'

const app = createApp(App);
const pinia = createPinia();

pinia.use(piniaPluginPersistedstate)
app.use(pinia);

app.mount("#app");

不要忘记命名存储。存储的名称用于为存储给予密钥。例如：

import { defineStore } from 'pinia'

    export const useStore = defineStore('nameOfStore', {
      state: () => {
        return {
          someState: 'hello pinia',
        }
      },
      persist: true,
    })

localStorage（如果使用默认存储系统）的键为“NameOfStore”，值为“{someState：“你好，皮尼亚”}

我们

如果不想使用Pinia，可以使用https://vueuse.org/中实用程序。
npm i @使用/核心

*main.js*
import { createPinia } from 'pinia'
createApp(App).use(createPinia()).mount('#app')
*store.js*
import { useStorage } from '@vueuse/core'
state: () => {
        return {
          someState: useStorage(someState: 'hello pinia'),
        }

用法：https://vueuse.org/core/useStorage/#usage