JSFiddle - React, Tailwind, and code Playground

HTML

<select id="select_street">
  <option value="1">Street 1</option>
  <option value="2">Street 2</option>
  <option value="3">Street 3</option>
  <option value="4">Street 4</option>
</select>
<input type="text" id="search_filter" />

JavaScript

$("#search_filter").on('keyup', function(e) {
  $("#select_street").attr('size', $("#select_street option").length);
  $("#select_street option").each(function() {
    if ($(this).html().toLowerCase().includes($.trim($('#search_filter').val()).toLowerCase())) {
      $(this).show();
    } else {
      $(this).hide();
    }
  });
});