HTMLMeterElement.labels

var labelElements = meter.labels;

<label id="label1" for="test">Label 1</label>
<meter id="test" min="0" max="100" value="70">70</meter>
<label id="label2" for="test">Label 2</label>

window.addEventListener("DOMContentLoaded", function() {
  const meter = document.getElementById("test");
  for(var i = 0; i < meter.labels.length; i++) {
    console.log(meter.labels[i].textContent); // "Label 1" and "Label 2"
  }
});