You can do the gradient differently and animate the position. The trick is to double the size of the gradient and make the value of color stop half of their actual values so you keep the same visual gradient then you can animate it from left to right.
It won't look exactly the same as the gradient you defined in the animation due to the calculation of farthest-corner.
#shine-div {
height: 30vh;
width: 60vw;
margin-right: auto;
margin-left: auto;
border-radius: 10px;
background: radial-gradient(farthest-corner at top, #FFFFFF 0%, #ffb3ff 4%, #ff33ff 12.25%, #800080 31.25%, #b300b3 50%) top right/200% 200%;
display: flex;
justify-content: center;
align-items: center;
color: white;
font-weight: bold;
animation: colorChange 5s infinite alternate;
}
@keyframes colorChange {
to {
background-position:top left;
}
}
<div id="shine-div">
Shine
</div>
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