CE backport for gitlab-org/gitlab-ee!14700 (Export design repository in project export)

What does this MR do?

Issue https://gitlab.com/gitlab-org/gitlab-ee/issues/11090

This MR is the CE backport for https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/14700

This MR targets https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/30834, which contains the docs and changelog changes.

This MR will be merged into https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/30834 when it passes its reviews.

Does this MR meet the acceptance criteria?

Conformity

• [-] Changelog entry for user-facing changes, or community contribution. Check the link for other scenarios.
• [-] 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