Not just immobilisation/myorelaxation, but true general anaesthesia (although not very deep). Isoflurane was used as inhalation anaesthetic. Swan on photo is recovering after anaesthesia.
As I remember, intubation in anaesthetised birds is necessary during complex and invasive surgery. In other cases of anaesthesia the intubation is optional. Pinioning is considered by zoo vets as short, easy and somewhat routine procedure, so intubation is not required. These birds were not intubated during any stage of surgery.