Apply styles from vue files in shadow DOM

index.js

// Set shadowRoot in root Vue options

new Vue({
  el: $root,
  shadowRoot: yourShadowRoot,
  components: { App },
  render: (h: any) => h('App')
} as any)

webpack.config.js

// Set `shadowMode` in options of both vue-loader and vue-style-loader

config = {
  module: {
    rules: [
      {
        test: /\.vue$/,
        loader: 'vue-loader',
        options: {
          shadowMode: true
        }
      },
      {
        test: /\.scss$/,
        use: [
          { loader: 'vue-style-loader', options: { shadowMode: true } },
          'css-loader',
          'postcss-loader',
          'sass-loader'
        ]
      },
    ]
  }
}