Missing Labels on "Add new group"

1) That path is part of the fieldable panels panes module, not Panels.
2) That path is actually handled by core's Field UI module, the same way that the manage display page for content types is. All Fieldable Panels Panes does is provide the menu entry and associated setup, and field UI renders the page from it. Any flaws it has should be shared by the manage display page for any (node) content type.

This is the entirety of the code in this module that handles those paths:

          'admin' => array(
            'path' => 'admin/structure/fieldable-panels-panes/manage/%fieldable_panels_panes_type',
            'bundle argument' => 4,
            'real path' => 'admin/structure/fieldable-panels-panes/manage/fieldable-panels-pane',
            'access arguments' => array('administer fieldable panels panes'),
          ),

(Note that in the latest release the path has changed slightly from earlier releases).

That's in fieldable_panels_panes_entity_info(). The field_ui module takes that data and makes tabs out of it and it fully handles those tabs. Why those act different I am not sure. It may be possible that there's some other data in hook_entity_info that we're missing, but if so I am unfamiliar with it.

The field_ui module takes that data and creates the tabs

I'm glad I was able to help you track it down!

Thx for noticing this. The patch has been committed to dev.