Modification points:

• In your Google Apps Script side, the blob is returned to Javascript side. Unfortunately, in the current stage, the blob of Google Apps Script cannot be directly used on the Javascript side. I thought that this might be the reason for your issue.

In your situation, how about the following modification?

Modified script:

Google Apps Script side:

From:

return blob

To:

return `data:${blob.getContentType()};base64,${Utilities.base64Encode(blob.getBytes())}`;

HTML&Javascript side:

From:

function showGraph(blob){

  var url = window.URL.createObjectURL(blob);
  document.getElementById("graph").src = url

}

To:

function showGraph(url){
  document.getElementById("graph").src = url
}

• In this modification, it supposes that the tag like <img id="graph"> is existing in your HTML. Please be careful this.

Reference:

• base64Encode(data)

Added:

From graph of document.getElementById("graph"), I thought that you might want to show the image. But, if you want to make user download the file from Google Apps Script, how about the following modification?

Modified script:

Google Apps Script side:

From:

return blob

To:

return [`data:${blob.getContentType()};base64,${Utilities.base64Encode(blob.getBytes())}`, blob.getName()];

HTML&Javascript side:

<input type="button" value="download" onclick="sample()">

<script>
function sample() {
  google.script.run.withSuccessHandler(showGraph).withFailureHandler(onFailure).retrieveAdmiraltyTideGraph(selectedStation, dateFrom, numDays);
}

function showGraph([url, filename]){
  fetch(url)
  .then(res => res.blob())
  .then(blob => {
    var a = document.createElement("a");
    var url = window.URL.createObjectURL(blob);
    a.href = url;
    a.download = filename;
    a.click();
  });
}

function onFailure(e) {
  console.log(e)
}

• In this modification, when the button is clicked, the file is downloaded by retrieving the data from Google Apps Script.
• In this case, please set the variables of selectedStation, dateFrom, numDays at Javascript side.