import ClickAwayListener from '@mui/base/ClickAwayListener';
...
<ClickAwayListener onClickAway={handleClickAway}>
<div>
<button type="button" onClick={handleClick}>
Open menu dropdown
</button>
{open ? (
<Portal>
<Box sx={styles}>
Click me, I will stay visible until you click outside.
</Box>
</Portal>
) : null}
</div>
</ClickAwayListener>