WIP: CE backport for gitlab-org/gitlab-ee!14702 (Export design management data with project export)

What does this MR do?

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

This is the CE backport of https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/14702. 💬 Discussion on this MR should ideally take place there.

A separate MR https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/30928 contains changes to support the project's design repository. This MR will remain a WIP: until https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/30928 is merged into this MR.

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