您应该使用Promises或async/await处理此问题。
下面是一个例子：

document.getElementById("insert").addEventListener(
  "click",
  async function (event) {
    event.preventDefault();
    var spinner = document.getElementById("spinner");
    spinner.style.display = "";
    await insertDataToDatabase(results.data);
    spinner.style.display = "none";
  },
  false
);

async function insertDataToDatabase(data) {
  data_noheader = data.slice(1);

  for (i = 0; i < data_noheader.length; i++) {
    await $.ajax({
      url: "index.php",
      type: "POST",
      dataType: "json",
      data: {
        action: "import",
        data: data_noheader[i],
      },
      success: function (response) {},
      error: function (response) {},
    });
  }
}

或者更好一点的解决方案：

document.getElementById("insert").addEventListener(
  "click",
  async function (event) {
    event.preventDefault();
    var spinner = document.getElementById("spinner");
    spinner.style.display = "";
    await insertDataToDatabase(results.data);
    spinner.style.display = "none";
  },
  false
);

async function insertDataToDatabase(data) {
  data_noheader = data.slice(1);

  await Promise.all(data_noheader.map((row) => {
    return $.ajax({
      url: "index.php",
      type: "POST",
      dataType: "json",
      data: {
        action: "import",
        data: row,
      },
      success: function (response) {},
      error: function (response) {},
    });
  }));
}