For an app created with create-react-app I managed to see the version:
- Open Chrome Dev Tools / Firefox Dev Tools,
- Search and open main.XXXXXXXX.js file where XXXXXXXX is a builds hash /could be different,
- Optional: format source by clicking on the {} to show the formatted source,
- Search as text inside the source for react-dom,
- in Chrome was found: "react-dom": "^16.4.0",
- in Firefox was found: 'react-dom': '^16.4.0'
The app was deployed without source map.