@click.stop not trigger the click event on document.addEventListener

[Chhunneng]

As I check the vue-emoji-picker can only use @click.stop to open the picker. I also have another popover and my purpose is I want to close the popover when click to open the picker but it can not trigger a click when I click to open the picker. Is there any way to close my popover before the picker is open?
Noted: my popover is triggered by add event click to document and the click is outside my popover.