The admin sidebar was kind of a mess. It used the class names and styles

from the admin widgets, but then did a bunch of overrides and other

element-specific styles. This change breaks it apart and makes it so that

future redesign work will be much easier.
This involves several pieces:

Renaming the template so it doesn't claim to be a widget.
Switching away from the .admin-widget class and associated

  sub-element classes, and moving towards our new CSS naming standards.
Defining new rules for the new classes, bringing across only those

  things which are necessary for the look of the sidebar.
Eliminating style rules specific to each section of the sidebar and

  making those general.

There is one visual change in here, removing the text from the "Add"

links within the "Manage" section. This text really doesn't add anything

to the user experience, and it cluttered up both the visual appearance

and the style rules. I've moved this into a tooltip instead (and changed

it to say "Add new").

Verified the visual appearance and behavior of the admin sidebar.