Refactor Design management application to match new visual styles

What does this MR do?

This MR is a part of the work for moving Design Management app to the Issue description. Here we change visual styles of the moved app to match designs. Please be mindful that we work on this migration behind the feature flag. If you want to test changes locally, please be sure to run the following code in the Rails console:

Feature.enable(:design_management_moved)

Change	MR
Create a new Design Management app to be displayed behind the feature flag	!34932 (merged)
Refactor Design Management app to be displayed on the Issue instead of tabs	!35042 (merged)
Refactor Design management application to match new visual styles	👉🏻 You are here
Update Design Management documentation	TBD
Make a cleanup after Design Management feature flag is removed	TBD

Screenshots

new

Conformity

• Code review guidelines
• Merge request performance guidelines
• Style guides

Availability and Testing

• Review and add/update tests for this feature/bug. Consider all test levels. See the Test Planning Process.
• Tested in all supported browsers

Closes #223194 (closed)