how to give types to a $plugin under nuxtApp?

export type AppPlugin = {
    error(v: { code: string; error: any }): void
}

export default defineNuxtPlugin((nuxtApp) => {
    const appObject = {
        error(v) {
            // todo: make better error handling
            console.error(`[APP|ERROR] error at ${v.code}: ${v.error}`)
        },
    } as AppPlugin

    nuxtApp.provide('app', appObject)
})

import type { AppPlugin } from '../plugins/app'
import type { ApolloClient } from '@apollo/client/core'

declare module '#app' {
    interface NuxtApp {
        $app: AppPlugin
        $apollo: ApolloClient
    }
}