Hi there, if you still need, I found a thread that I think will be helpful to you. In that, several options are discussed but they generally involve recording how long it takes to download an image file. I adapted the code from user john Smith in that thread to perform a speedtest and capture the value in an embedded data field each time a button is clicked.
To give it a try, first create an Embedded Data element called "speed" and put it at the top of the Survey Flow.
Next, create a Text/Graphic question and use the Rich Content Editor's HTML/Source view "<>" to update the Question Text with the below.
Click to write the question text



Click to test speed



Speed: 0
Finally, add the below to the question's JavaScript in the OnReady section:
var speed=0;

document.getElementById("button1").onclick=function(){

var testConnectionSpeed = {
  imageAddr : "https://upload.wikimedia.org/wikipedia/commons/a/a6/Brandenburger_Tor_abends.jpg", // this is just an example, you rather want an image hosted on your server
  downloadSize : 2707459, // Must match the file above (from your server ideally)
  run:function(mbps_max,cb_gt,cb_lt){
    testConnectionSpeed.mbps_max = parseFloat(mbps_max) ? parseFloat(mbps_max) : 0;
    testConnectionSpeed.cb_gt = cb_gt;
    testConnectionSpeed.cb_lt = cb_lt;
    testConnectionSpeed.InitiateSpeedDetection();
  },
  InitiateSpeedDetection: function() {
    window.setTimeout(testConnectionSpeed.MeasureConnectionSpeed, 1);
  },
  result:function(){
    var duration = (endTime - startTime) / 1000;
    var bitsLoaded = testConnectionSpeed.downloadSize * 8;
    var speedBps = (bitsLoaded / duration).toFixed(2);
    var speedKbps = (speedBps / 1024).toFixed(2);
    var speedMbps = (speedKbps / 1024).toFixed(2);
    if(speedMbps >= (testConnectionSpeed.max_mbps ? testConnectionSpeed.max_mbps : 1) ){
      testConnectionSpeed.cb_gt ? testConnectionSpeed.cb_gt(speedMbps) : false;
    }else {
      testConnectionSpeed.cb_lt ? testConnectionSpeed.cb_lt(speedMbps) : false;
    }
  },
  MeasureConnectionSpeed:function() {
    var download = new Image();
    download.onload = function () {
        endTime = (new Date()).getTime();
        testConnectionSpeed.result();
    }
    startTime = (new Date()).getTime();
    var cacheBuster = "?nnn=" + startTime;
    download.src = testConnectionSpeed.imageAddr + cacheBuster;
  }
}


testConnectionSpeed.run(1.5, function(mbps){
console.log(mbps+"Mbps"),
speed = mbps+"Mbps",
document.getElementById("speed").innerHTML=speed,
Qualtrics.SurveyEngine.setEmbeddedData('speed', speed)
})


}