JSFiddle - React, Tailwind, and code Playground

HTML

<select id="menlist" name="menlist">
  <option value="1">Sausis</option>
  <option value="2">Vasaris</option>
  <option value="3">Kovas</option>
  <option value="4">Balandis</option>
  <option value="aa">Name aa</option>
  <option value="bb">Name bb</option>
</select>
<select id="menlist2" name="menlist2">
  <option value="1">Sausis</option>
  <option value="2">Vasaris</option>
  <option value="3">Kovas</option>
  <option value="4">Balandis</option>
  <option value="aa">Name aa</option>
  <option value="bb">Name bb</option>
</select>

JavaScript

$(function(){
    $("#menlist").keyup(function(){
        var value=$(this).val();
       
        $("#menlist2 option[selected]").attr("selected", "selected");
    });
    $("#menlist").change(function(){
        $("#menlist2").val($(this).val());
    });
});