DOM XSS JQuery Selector CTF

Question

I found the below JS script in the CTF website's source code. If I understand the script correctly, after the website is loaded, getParameterByName function is called which returns the value of focus URL parameter. Subsequently, the value is treated as a selector on which focus() function is called. So for example, appending ?focus=#search to the base URL highlights the input with id 'search'.

function getParameterByName(name, url) {
  if (!url) url = window.location.href;
  name = name.replace(/[\[\]]/g, "\\$&");
  var regex = new RegExp("[?&]" + name + "(=([^&#]*)|&|#|$)"),
  results = regex.exec(url);
  if (!results) return null;
  if (!results[2]) return '';
  return decodeURIComponent(results[2].replace(/\+/g, " "));
}

$(document).ready(function() {
  // Focus field specified in focus column
  var selector = getParameterByName("focus");
  $(selector).focus()

  // Override submit functio
  $("#search_form").submit(function(e) {
    $("#output").text("submitting");
    var form = $(this);
    var url = form.attr('action');
    $.ajax({
      type: "POST",
      url: url,
      data: form.serialize(),
      // serializes the form's elements.
      success: function(data) {
        $("#output").text(data);
      }
    });

    e.preventDefault(); // avoid to execute the actual submit of the form.
  });
});

I've tried modifying the URL with passing an input element with onFocus but without success. https://example.org/?focus=<input type='text' onFocus='alert(1)'>

Also, tried escaping the string to call the alert inside the focus. https://example.org/?focus=#search").focus(function(){alert(1)});).focus()

Or adding onFocus attribute. https://example.org/?focus=#search").attr('onFocus', 'alert(1)').focus();

All the above attempts failed. I searched Google for JQuery selector sink but I didn't find anything useful. Can you please point out what am I doing wrong?