firstPHP/public/js/ajax.js

function ajaxRequest() {
   const request = new XMLHttpRequest();
   request.open("POST", "handler");
   request.addEventListener("load", () => {
      const responseText = request.responseText;
      const targetElement = document.getElementById("buttonAdd");
      const divElement = document.createElement("div");
      divElement.classList.add("form-control");
      divElement.style.backgroundColor = "#bbbbbb"; // Задайте здесь свой нужный стиль
      divElement.innerHTML = responseText;
      targetElement.insertAdjacentElement("beforebegin", divElement);

   });
   request.send();
}