Just for completenes sake, image-set is the way to set webp background-image with fallback:
.some-class {
background-image: url('fallback-image.png');
background-image: image-set(
url('image.webp') 1x,
url('image@2x.webp') 2x,
url('fallback-image.png') 1x,
url('fallback-image@2x.png') 2x
);
}
The webkit-prefix might have to be used depending on the browser. And to this day firefox does not seem to support it. Check out caniuse for more info.
Edit: Just tried it myself in firefox and the webkit-prefix seems to work. This just shows that one should rather trust the official docs and test it yourself.