Using linear-gradient in an animation on CSS

To fill linear-gradient, you will have to add linearGradient node inside the definitions section of your SVG file like below: (Read More about Linear Gradient)

<defs>
    <linearGradient id="FillGradient" gradientTransform="rotate(90)">
      <stop offset="2%" stop-color="#FFF" />
      <stop offset="95%" stop-color="#9356DC" />
    </linearGradient>
</defs>

Make sure you are adding id attribute which is going to be used in CSS to fill the gradient like below:

@keyframes fill-animation {
  0%{
     fill-opacity: 0.1;
  }
  10% {
     fill: url(#FillGradient);
     fill-opacity: 0.1;
  }
  80% {
     fill: url(#FillGradient);
     fill-opacity: 1;
  }
  100% {
     fill: url(#FillGradient);
     fill-opacity: 1;
  }
}

You can remove the fill-opacity and of course change the color of gradient in linearGradient node as per your need.

See the working Snippet below: (I have commented few styles just to make it big and clear)

.icon {
  fill: transparent;
  stroke: black;
  stroke-width: 50;
  cursor: pointer;
 /* position: absolute;
  right: 1.5rem;
  bottom: 2rem;*/
}

.icon svg {
  overflow: visible;
  width: 5.6rem; /* changed from 1.6 to 5.6 */
}

.icon .heart-main:active path {
  animation: fill-animation 1.5s ease-in-out forwards;
  stroke: #9356DC;
}

@keyframes fill-animation {
  0%{
     fill-opacity: 0.1;
  }
  10% {
     fill: url(#FillGradient);
     fill-opacity: 0.1;
  }
  80% {
     fill: url(#FillGradient);
     fill-opacity: 1;
  }
  100% {
     fill: url(#FillGradient);
     fill-opacity: 1;
  }
}

<div class="icon">
   <svg class="heart-main" viewBox="0 0 512 512" width="300" title="heart">
      <path d="M462.3 62.6C407.5 15.9 326 24.3 275.7 76.2L256 96.5l-19.7-20.3C186.1 24.3 104.5 15.9 49.7 62.6c-62.8 53.6-66.1 149.8-9.9 207.9l193.5 199.8c12.5 12.9 32.8 12.9 45.3 0l193.5-199.8c56.3-58.1 53-154.3-9.8-207.9z" />
      <defs>
        <linearGradient id="FillGradient" gradientTransform="rotate(90)">
          <stop offset="2%" stop-color="#FFF" />
          <stop offset="98%" stop-color="#9356DC" />
        </linearGradient>
      </defs>
   </svg>
</div>

you could use my code

        @keyframes value {
        0%{background-image: linear-gradient(90deg, red, purple, green);}
        25%{background-image: linear-gradient(90deg, orange, yellow,blue);}
        50%{background-image: linear-gradient(90deg, black, grey, white);}
        100%{background-image: linear-gradient(90deg,lime,violet,magenta);}
        }

then use

       .icon{
        animation-name: value;
        animation-duration: 50s;
        animation-iteration-count: infinite;
        }

you could use background-image instead of fill and if that doesn't work you could use color instead. i hope i helped but i am pretty new to css myself.