JSFiddle - React, Tailwind, and code Playground

HTML

<div class="c-add-task-main-container">
    <h2 class="c-add-task-title">Time Tracker</h2>
    <button class="start">Start</button>
    <button class="clear">Clear</button>
    <div class="output">00:00:00</div>
</div>

<div class="c-add-task-main-container">
    <h2 class="c-add-task-title">Time Tracker</h2>
    <button class="start">Start</button>
    <button class="clear">Clear</button>
    <div class="output">00:00:00</div>
</div>

JavaScript

let startTimeButtons = document.querySelectorAll(".start")

let seconds = [-1, -1];
let interval = [];
if (localStorage.getItem("stopwatchSeconds") != null) {
  seconds = JSON.parse(localStorage.getItem("stopwatchSeconds"));
  seconds = seconds.map(n => parseInt(n))
}

const timer = (el, i) => {
  seconds[i]++;
  localStorage.setItem("stopwatchSeconds", JSON.stringify(seconds));
  // Get hours
  let hours = Math.floor(seconds[i] / 3600).toString().padStart(2, 0);
  // Get minutes
  let minutes = Math.floor((seconds[i] - hours * 3600) / 60).toString().padStart(2, 0);
  // Get seconds
  let secs = Math.floor(seconds[i] % 60).toString().padStart(2, 0);

  el.parentElement.querySelector('.output').innerHTML = `${hours}:${minutes}:${secs}`;

};

startTimeButtons.forEach((btn, index) => {
  timer(btn, index); // update time on page load
  btn.addEventListener("click", () => {
    if (btn.textContent == 'Start') {
      btn.textContent = 'Pause';
      interval[index] = setInterval(timer, 1000, btn, index);
    } else {
      btn.textContent = 'Start';
      clearInterval(interval[index]);
    }
  });
})