What sort of brain injury is from a bleed from an neurosurgery operation traumatic or acquired?

Both: It depends on the reason why the surgery was done. You can have a traumatic bleed that need to evacuated or decompressed to prevent brain herniation. Intracranial bleed can also be due to a vascular malformation, anurysm, coagulopathy, medications or complication of surgery for brain tumor.

Iatrogenic: An injury or problem or disease caused by the activity of a healthcare worker, especially a physician and especially if it's preventable is called iatrogenic.

Depends: If someone has an emergency surgery due to trauma or a brain hemorrhage and has either recurrent bleeding or bleeding in another area or is on anticoagulants, it would be considered a complication of the surgery and due to the initial pathology.