Next to the company managed projects (formerly classic projects) you can also choose team-managed projects (formerly next-gen projects) in Jira Cloud. Synchronizing with team-managed projects is possible with Backbone, and configuring the synchronization works as with any other project. You can synchronize a project on data center to team-managed and also synchronize with different types of projects (e.g. service projects, software projects).
There are, however, a few features that do not yet work:
https://k15t.jira.com/issues/?jql=project+%3D+BAC+AND+%28summary+%7E+%22next-gen%22++OR+key+%3D+BAC-1359%29++order+by+key++++++
If you run into any other issue with synchronizing team-managed projects, or have other questions, then please contact our support.