Ensure existing group exports are removed in API

Call the same service in the group export API as the controller for the
frontend. This keeps the consistency with the UI functionality.

Relates to: https://gitlab.com/gitlab-org/gitlab/-/issues/211805

lib/api/group_export.rb

@@ -27,9 +27,13 @@ module API
         detail 'This feature was introduced in GitLab 12.5.'
       end
       post ':id/export' do
-        GroupExportWorker.perform_async(current_user.id, user_group.id, params) # rubocop:disable CodeReuse/Worker
+        export_service = ::Groups::ImportExport::ExportService.new(group: user_group, user: current_user)
 
-        accepted!
+        if export_service.async_execute
+          accepted!
+        else
+          render_api_error!(message: 'Group export could not be started.')
+        end
       end
     end
   end

spec/requests/api/group_export_spec.rb

@@ -102,6 +102,19 @@ describe API::GroupExport do
         end
       end
 
+      context 'when the export cannot be started' do
+        before do
+          group.add_owner(user)
+          allow(GroupExportWorker).to receive(:perform_async).and_return(nil)
+        end
+
+        it 'returns an error' do
+          post api(path, user)
+
+          expect(response).to have_gitlab_http_status(:error)
+        end
+      end
+
       context 'when user is not a group owner' do
         before do
           group.add_developer(user)