error caught during app initialization TypeError: Cannot set property $pinia of #<Object> which has only a getter

[Lionberg]

Reproduction

impossible to add nuxt.config.ts in playground

Steps to reproduce the bug

Follow instructions at the docs: https://pinia.vuejs.org/ssr/nuxt.html

1. install:
   npx nuxi@latest module add pinia

2. add to package.json:
   "overrides": {
   "vue": "latest"
   }

3. // nuxt.config.js
   export default defineNuxtConfig({
   // ... other options
   modules: [
   // ...
   '@pinia/nuxt',
   ],
   })

4. Get the error in console:
   error caught during app initialization TypeError: Cannot set property $pinia of # which has only a getter

   P.S. These instructions says nothing about creating plugin and defining a store. Maybe docs needs a link there?

   Expected behavior

   use your store as usual

   Actual behavior

   impossible to use your store as usual -- client error, and error in nuxt: Cannot set property $pinia of # which has only a getter

   Additional information

   removing '@pinia/nuxt' from modules solves the issue.
   But pinia does not keep state during page refreshes