An anesthetic would typically consist of something like a small dose of a short-acting benzo before surgery for anxiety, propofol (very short acting) for induct

An anesthetic would typically consist of something like a small dose of a short-acting benzo before surgery for anxiety, propofol (very short acting) for induction, an opioid for pain management, an anesthetic gas like sevoflurane to maintain anesthesia, pressors to bring up blood pressure if necessary, and a few other drugs that probably don't merit mention. Of these drugs, the only ones that might cause withdrawal symptoms would be the benzo or the opioid. The benzo, if it's even given at all, is going to be tiny. Even if we were to hypothesize that a single unusually large dose of an opioid could induce dependency, a surgery where the patient isn't even given opioids to take home wouldn't warrant such a dose in the OR. In short, your second-hand account makes no sense.