Regarding to the typing, you can fix by removing namespace import since generated typing is now exporting default value. You just simply import as default import:

import styles from "./App.css";

<h3 className={styles["background"]}>CSS Here</h3>

Plus, in order to have css getting appended in your document, you might have to use style-loader.

For the parsing error, it’s most likely related to your linter, so try to have a look the way you set it up.