Running

esbuild index.css --bundle --outdir=build --entry-names=styles/[name] --asset-names=assets/[name] --loader:.png=file

with index.css looking like

.foobar {
    background-image: url(./foobar.png);
}

results in build/styles/index.css:

/* index.css */
.foobar {
  background-image: url(./assets/foobar.png);
}

Since foobar.png is copied to build/assets/foobar.png the URL should actually be ../assets/foobar.png?