JSFiddle - React, Tailwind, and code Playground

HTML

<input type="button" id="start" value="Отправить">

<br>
<output id="out"></output>

CSS

output {
  font-family: monospace;
  white-space: pre;
}

JavaScript

var btn = document.getElementById('start');

btn.addEventListener('click', function(){
  btn.value = "start"; //проблема тут
  out.textContent += 'start ' + +new Date() + '\n'
  
  var xhr = new XMLHttpRequest();
  xhr.open('POST', '/echo/json/', false);
  xhr.onload = function(e){
    if(xhr.readyState == 4 && xhr.status == 200){
      btn.value = "ready";
  out.textContent += 'ready ' + +new Date() + '\n'
    }
  };
  xhr.send();
});