Export design repository in project export

What does this MR do?

Issue #11090 (closed)

This MR targets https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/14702, which contains the docs and changelog changes.

This MR will be merged into https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/14702 when it passes its reviews.

CE backport https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/30928

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry
• [-] Documentation created/updated or follow-up review issue created
• Code review guidelines
• Merge request performance guidelines
• Style guides
• [-] Database guides
• Separation of EE specific content

Performance 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