How to apply a gradient to the color instead of a solid color value

const FULL_DASH_ARRAY = 283;

const TIME_LIMIT = 20;
let timePassed = 0;
let timeLeft = TIME_LIMIT;
let timerInterval = null;

document.getElementById("app").innerHTML = `
<div class="base-timer">
  <svg class="base-timer__svg" viewBox="0 0 100 100" xmlns="http://www.w3.org/2000/svg">
   <defs>
   <linearGradient id="linear" x1="0%" y1="0%" x2="100%" y2="0%">
     <stop offset="0%"   stop-color="#05a"/>
     <stop offset="50%"  stop-color="#a55"/>
     <stop offset="100%" stop-color="#0a5"/>
   </linearGradient>
 </defs>
    <g class="base-timer__circle">
      <circle class="base-timer__path-elapsed" cx="50" cy="50" r="45"></circle>
      <path
        
        id="base-timer-path-remaining"
        stroke=url(#linear)
        stroke-dasharray="283"
        
        class="base-timer__path-remaining green"
        d="
          M 50, 50
          m -45, 0
          a 45,45 0 1,0 90,0
          a 45,45 0 1,0 -90,0
        "
      ></path>
    </g>
  </svg>
  <span id="base-timer-label" class="base-timer__label">${formatTime(
    timeLeft
  )}</span>
</div>
`;

startTimer();

function onTimesUp() {
  clearInterval(timerInterval);
}

function startTimer() {
  timerInterval = setInterval(() => {
    timePassed = timePassed += 1;
    timeLeft = TIME_LIMIT - timePassed;
    document.getElementById("base-timer-label").innerHTML = formatTime(
      timeLeft
    );
    setCircleDasharray();

    if (timeLeft === 0) {
      onTimesUp();
    }
  }, 1000);
}

function formatTime(time) {
  const minutes = Math.floor(time / 60);
  let seconds = time % 60;

  if (seconds < 10) {
    seconds = `0${seconds}`;
  }

  return `${minutes}:${seconds}`;
}



function calculateTimeFraction() {
  const rawTimeFraction = timeLeft / TIME_LIMIT;
  return rawTimeFraction - (1 / TIME_LIMIT) * (1 - rawTimeFraction);
}

function setCircleDasharray() {
  const circleDasharray = `${(
    calculateTimeFraction() * FULL_DASH_ARRAY
  ).toFixed(0)} 283`;
  document
    .getElementById("base-timer-path-remaining")
    .setAttribute("stroke-dasharray", circleDasharray);
}

body {
  font-family: sans-serif;
  display: grid;
  height: 100vh;
  place-items: center;
}

.base-timer {
  position: relative;
  width: 300px;
  height: 300px;
}

.base-timer__svg {
  transform: scaleX(-1);
}

.base-timer__circle {
  fill: none;
  stroke: none;
}

.base-timer__path-elapsed {
  stroke-width: 7px;
  stroke: grey;
}

.base-timer__path-remaining {
  stroke-width: 7px;
  stroke-linecap: round;
  transform: rotate(90deg);
  transform-origin: center;
  transition: 1s linear all;
  fill-rule: nonzero;
}

.base-timer__path-remaining.green {
  /*/color: rgb(65, 184, 131);*/
  /*stroke: red;*/
}

.base-timer__label {
  position: absolute;
  width: 300px;
  height: 300px;
  top: 0;
  display: flex;
  align-items: center;
  justify-content: center;
  font-size: 48px;
}

<div id="app"></div>