JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<select id="select">
 
</select>
<button>
Добавить 
</button>

JavaScript

let container=$('#select'),
selects=new Proxy([],{
	set(array,key,value,proxy){
  	if(array.includes(value)) return
    array[key]=value
    $('<option>',{value}).text(value).appendTo(container)
  }
})
$('button').click(()=>selects.push(Math.random().toString(36).substring(2,5)))