feat(nuxt): remove wrong $nuxt in Nuxt 3

BREAKING CHANGE: in Nuxt 3, `$nuxt` is no longer available in stores.
This is because it was removed in Nuxt 3 and it is no longer the
_context_ as it used to be. Most of the features used there, like
`$fetch` are now globally available and therefore remove the need of it.
You can also use
[`useNuxtApp()`](https://v3.nuxtjs.org/bridge/bridge-composition-api/)
when necessary.

packages/nuxt/src/runtime/plugin.vue3.ts

@@ -6,12 +6,6 @@ export default defineNuxtPlugin((nuxtApp) => {
   nuxtApp.vueApp.use(pinia)
   setActivePinia(pinia)
 
-  // @ts-expect-error: _p is internal
-  pinia._p.push(({ store }) => {
-    // make it non enumerable so it avoids any serialization and devtools
-    Object.defineProperty(store, '$nuxt', { value: nuxtApp })
-  })
-
   if (process.server) {
     nuxtApp.payload.pinia = pinia.state.value
   } else if (nuxtApp.payload && nuxtApp.payload.pinia) {
@@ -25,13 +19,3 @@ export default defineNuxtPlugin((nuxtApp) => {
     },
   }
 })
-
-declare module 'pinia' {
-  export interface PiniaCustomProperties {
-    /**
-     * Nuxt context.
-     */
-    // FIXME: where is this type?
-    // $nuxt: import('@nuxt/types').Context
-  }
-}