Does React's npm run build add inline scripts in the build folder's index.html?

No, as of 11-May-2023, React does NOT add any inline scripts into the build folder's index.html file.

The build folder's index.html file includes an external JS file instead.

However in the previous versions before React 16 it did so, and still some third-party dependencies might do so as well. But React itself does not anymore.