Remove, refactor, and untangle Claro's CSS from Default Admin theme

Parent issue: #3582351: [Meta] Clean up CSS

Problem

The Default Admin theme is basically Gin renamed. Gin used Claro as a base theme, and that structure was flattened when it was added to core. To do this, Claro's CSS was copied en masse to the new theme.

Task

We need to go through and remove, refactor, and untangle the entirety of Claro's CSS to make the new theme maintainable. At this point I'm not sure if this will be one mega issue, or a series of smaller issues.