Charon
As the anesthesiologist you are the last face the patient sees on induction. You take care of them throughout the case. You are the first face they see upon waking. You roll them back to PACU.
You do this multiple times a day, in anesthesia. You become accustomed to this pattern.
The state of general anesthesia, in certain ways, resembles death more than it does sleep. One of my professors remarked that we bring the patient to "the banks of the River Styx." Every induction, a type of death. Every emergence - resurrection.
Organ procurement is different. For one, there is no anesthetic "induction" - in these cases the patients are intubated and brain-dead, transported from the ICU. And though you roll the patient back to the OR, you won't be bringing them back.
Your job, as always, is to keep them "stable." Which is to say, you make sure their body keeps working while a series of surgeons removes their organs one by one, from least- to most- vital. This is clinically challenging, and can take hours. But at some point they will remove the heart and lungs. And then you are dismissed, because your services are no longer necessary, and the patient does not need you anymore.
Is there a new lightness to the room? The sense that a soul has left? I have searched and searched and never felt it. But I like to believe that you leave the room as the soul does. Their guide, like Charon. To carry them away.