The z-index of #p-personal is set to 100 and thus it renders over the dialog. I understand that OOjs shouldn't be making mediawiki specific changes like this, but right now OO.uiDialog has a z-index of just 2. Is this something we might change?
VE handles it by creating an extra .ve-ui-overlay-global with a z-index of 101.
See also - https://www.mediawiki.org/wiki/Manual:Coding_conventions/CSS#z-index