New UI: where can I find the playbooks?

Playbooks haven't moved. In Cockpit > click the small chevron icon on the left to expose the sub-pages of Cockpit and you'll see Playbooks.

I had the same problem:

From Support: 
This looks to be an issue with your user not having any standard permission sets. When we add new components we upgrade only our stand permissions sets. To resolve this issue, we either need to assign you one of the standard permission sets (Admin or Standard, you do not want to use the cloned version), or you can manually add 'Workflowchild' Visual force page in the custom permission sets.

Thanks Lila, I've found it in the Cockpit section!