According to this page (https://docs.backdropcms.org/documentation/features-added-to-core), Views Bulk Operations has been added to core.
Was this a partial integration or has all the functionality of the Drupal 7 version of the module been integrated into core?
Not all the functionality has been integrated. Some missing features are listed in the meta issue https://github.com/backdrop/backdrop-issues/issues/3797 .
As of 2023, there is a contrib port of the full D7 Views Bulk Operations.
Ir includes the actions missing in the core's Bulk Operations, including configurable actions that allow to send emails, or set values for entity fields. It integrates seamlessly with Rules components, allowing to pass entity IDs to those components. VBO is easier to extend with custom actions.
It also is able to run all actions provided by core. This means that your View could just use VBO instead of core Operations, and still be able to do all things core Operations did.
Users interested in View Bulk Operations may also find the URL Publish and Unpublish module helpful. Gives a link in views (but also elsewhere) to publish and unpublish nodes.
Not all the functionality has been integrated. Some missing features are listed in the meta issue https://github.com/backdrop/backdrop-issues/issues/3797 .