The popup widget currently has no padding:
The PopupButtonWidget is created in popup/init.js:
button = new OO.ui.PopupButtonWidget( { icon: 'info', framed: false, classes: [ 'ext-ipinfo-button' ] } );
We can add padding by adding:
button = new OO.ui.PopupButtonWidget( { ..., popup: { padded: true } } );
...as described in the PopupButtonWidget documentation.