For React SVG background images, I find this works best:
// MyComponent.js
import mySvg from './mySvg.svg';
...
function MyComponent() {
return (
<div
className="someClassName"
style={{ backgroundImage: `url(${mySvg})` }}
>
... etc
The path to the SVG file will change when webpack bundles, so by using the template string you can keep things linked up.
In the CSS class you can do whatever styling you like.