document.activeElement condition won't work (with id or ref inside a div element)

I'm trying to make a menu and that when pressing outside of it it will get closed and will active clearTimeout so it won't get close again if re-opened.
Somehow when I press on the menu this condition is always true -

 if (document.activeElement !== menuRef.current) {//document.activeElement.id !==  'myField' 

<div ref={menuRef} id="myField"> is the wrapping div of the menu
So it doesn't work.
What am I doing here wrong ?

All in the codesandbox - Codesandbox

export default function Example() {
  const { toggleMenu } = useMenuState({ transition: true });
  let closeTimeMenu;
  const menuRef = useRef(null);

  useEffect(() => {
    function handleClickOutside() {
      setTimeout(() => {
        if (document.activeElement !== menuRef.current) {//document.activeElement.id !==  'myField' 
          console.log(" !== menuRef");
          clearTimeout(closeTimeMenu);
          window.onclick = toggleMenu(false);
        }
      }, 500);
    }

    document.addEventListener("mousedown", handleClickOutside);
    return () => {
      document.removeEventListener("mousedown", handleClickOutside);
    };
  }, []);

 
  function handleClick() {
    //menuRef.current.focus(); or - 
    document.getElementById('myField').focus();
   }
  

  function timeout() {
    closeTimeMenu = setTimeout(function () {
      toggleMenu(false);
    }, 1500);
  }

  return (
    <div ref={menuRef} id="myField">
      <button
        onMouseEnter={() => {
          toggleMenu(true);
          clearTimeout(closeTimeMenu);
        }}
        onMouseLeave={() => timeout()}
      >
        Hover to Open
      </button>

      <ControlledMenu
         anchorRef={menuRef}
        onMouseEnter={() => {
          toggleMenu(true);
          clearTimeout(closeTimeMenu);
        }}
         onItemClick={() => {
          handleClick();
          toggleMenu(false);
        }}
        onMouseLeave={() => timeout()}
      >
         <MenuItem>Save</MenuItem>
        <MenuItem>Close Window</MenuItem>
      </ControlledMenu>
    </div>
  );
}

Thanks