I've been trying to work this out too. I have text links and buttons I want to appear over the map, but when the pop-up appears I'd like it to appear over the text and buttons but I have not gotten it to honor the z-index. I can't tell if it just doesn't work the way I'd think or if I have the syntax wrong, or if it's some div hierarchy malarkey.
I'm trying to adjust it by setting the z-index of the .esri-popup__main-container css element. I've tried it with the text link div as a sibling of the map canvas div and as a child in addition to where it was originally, just above the main container the map canvas was inside. I think that'd be an Aunt/Uncle?
Anyway, it feels like no matter what I do the pop-up is always at the same z-index of the map canvas. Maybe the z-index only works internally for the position of API elements from other API elements? Is there maybe a simple example of using a z-index to add an element that's above the map but below the pop-up?
