BPF isn't showing up at all for cases created by a flow.
This flow creates cases and related accounts and contacts from a Dataverse entity that (in a separate flow) is pulling data from a constantly updated .xlsx stored in SharePoint.
The trigger for this flow that writes values from one Dataverse entity to these three other Dataverse entities is when a row is created in the Dataverse table. The actions are create new row in Case, create new row in Account, and create new row in Contact.
So the BPF enabled for this app is not showing up (it literally just isn't there) for these cases created with the flow, nor is the javascript for the page that controls tab visibility working.
However, the BPF and JS show up and work when a case is created manually.
(license = Dynamics for Customer Service)