Next to the company managed spaces (formerly classic spaces) you can also choose team-managed spaces (formerly next-gen spaces) in Jira Cloud. Synchronizing with team-managed spaces is possible with Backbone, and configuring the synchronization works as with any other space. You can synchronize a space on data center to team-managed and also synchronize with different types of spaces (e.g. service projects, software projects).
There are, however, a few features that do not yet work which you can find listed here. Besides that, Backbone can synchronize with a team-managed space, but it can't clone one. To sync with a team-managed space, create it in Jira first and select Sync an existing space.
If you run into any other issue with synchronizing team-managed spaces, or have other questions, then please contact our support.