Move Design Management routes, controllers to FOSS

What does this MR do?

This change is part of #212566 (closed) to move all Design Management code to FOSS.

This change moves the routes and controllers.

A changelog entry, and any documentation changes, will be added in the final MR.

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry
• [-] Documentation (if required)
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• Separation of EE specific content

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
• [-] Informed Infrastructure department of a default or new setting change, if applicable per definition of done