How to correctly build an npm package from Vue.component with nested components from other libraries?

Question

npm

I want to write my add-on for Vuetify components and publish it to npm. Decided to start simple.
The package itself has been published, you can import it into another project with Vuetify installed, everything is fine with that. Component example:

<template>
    <v-text-field outlined label="demo"></v-text-field>
</template>

<script>
    export default {
        name: "AirTextField",
    }
</script>

But when I try to connect it to another project and use it in a template, it says that v-text-field is not defined. Although literally a line above, I write my v-text-field component and it is displayed correctly.

What could be the reason?

Add- ons:

index.js (main code from offline Vue documentation)

import AirTextField from './components/AirTextField.vue';
import AirTextarea from './components/AirTextarea.vue';

export function install(Vue) {
    if (install.installed) return;
    install.installed = true;
    Vue.component('AirTextField', AirTextField);
    Vue.component('AirTextarea', AirTextarea);
}
const plugin = {
    install
};

let GlobalVue = null;
if (typeof window !== 'undefined') {
    GlobalVue = window.Vue;
} else if (typeof global !== 'undefined') {
    GlobalVue = global.Vue;
}
if (GlobalVue) {
    GlobalVue.use(plugin);
}

export {
    AirTextField,
    AirTextarea
}

package.json (packages and build method taken from another project, which also extends Vuetify's capabilities)

{
  "name": "airit-vue-components",
  "version": "1.0.3",
  "description": "",
  "author": "bubaley",
  "scripts": {
    "serve": "vue-cli-service serve",
    "build": "npm run build:browser && npm run build:es && npm run build:umd",
    "build:browser": "cross-env NODE_ENV=production rollup --config build/rollup.config.browser.js",
    "build:es": "cross-env NODE_ENV=production rollup --config build/rollup.config.es.js",
    "build:umd": "cross-env NODE_ENV=production rollup --config build/rollup.config.umd.js"
  },
  "main": "dist/airit-vue-components.umd.js",
  "module": "dist/airit-vue-components.esm.js",
  "unpkg": "dist/airit-vue-components.min.js",
  "files": [
    "dist/"
  ],
  "dependencies": {},
  "peerDependencies": {
    "core-js": "^3.6.5",
    "vuetify": ">=2.2.10"
  },
  "devDependencies": {
    "@vue/cli-plugin-babel": "^4.5.0",
    "@vue/cli-service": "^4.5.0",
    "cross-env": "^7.0.2",
    "rollup": "^1.10.0",
    "rollup-plugin-analyzer": "^3.0.0",
    "rollup-plugin-babel": "^4.3.2",
    "rollup-plugin-commonjs": "^9.3.4",
    "rollup-plugin-css-only": "^1.0.0",
    "rollup-plugin-node-resolve": "^4.2.3",
    "rollup-plugin-postcss": "^2.0.3",
    "rollup-plugin-replace": "^2.0.0",
    "rollup-plugin-terser": "^4.0.4",
    "rollup-plugin-vue": "^5.0.0",
    "sass": "^1.19.0",
    "sass-loader": "^8.0.0",
    "vue": "^2.6.11",
    "vue-cli-plugin-vuetify": "^2.0.8",
    "vue-template-compiler": "^2.6.11",
    "vuetify-loader": "^1.3.0"
  },
  "browserslist": [
    "> 1%",
    "last 2 versions",
    "not dead"
  ],
  "license": "MIT"
}

Answer 1

https://ru.vuejs.org/v2/guide/plugins.html#Create...
Instead of exporting the install function, export the plugin constant
And that is what you will need to give to Vue.use