Next 13 AppRoute - generate js for a third party use

Question

I am working on a widget made in Next 13 with app route. This widget is a JSX component. I need it to be able to be used as an embedded JS in another company's project as follows:

    <script src="https://my-url/my-component.js" type="text/javascript"></script>
    <script type="text/javascript">
      MyApp.init({
        some: "config"
      }); 
    </script>

How could this be done?

I tried to create a file like:

import { createRoot } from 'react-dom/client'
import MyComponent from '@/app/components/MyComponent'

export const init = (container, param1, param2, param3) => {
  createRoot(container).render(
    <MyComponent
      param1={param1}
      param2={param2}
      param3={param3}
    />
  )
}