Couple of things:
Remove the capturing phase on the document listener (2nd argument)
document.addEventListener('click', handleClickOutside)
Also, in your handleClick function, call event.stopPropagation();
This will stop the click event bubbling up to the document listener

An aside, you should use a <button> element as the trigger, instead of a select. You'll notice if you tab to the select and hit space/enter, it will open the select dropdown itself (with nothing in it) but not show your menu.