Example of using border image with border radius using a exclusion mask.

border-image-border-radius.css

.box {
  --radius: 3px;
  position: relative;
  width: 64px;
  height: 64px;
  background: linear-gradient(to bottom, green, gold);
  border-radius: var(--radius);
}

.box::after {
  content: "";
  position: absolute;
  inset: 0px;
  border-radius: var(--radius);
  border: 1px solid transparent;
  background: linear-gradient(to bottom, rgba(0, 0, 0, 0.08), rgba(0, 0, 0, 0.16)) border-box;
  -webkit-mask: linear-gradient(#fff 0 0) padding-box, linear-gradient(#fff 0 0);
  -webkit-mask-composite: xor;
  mask-composite: exclude;
}