General anesthesia can be inhalation of volatile liquid aesthetic agents requiring respiratory support, deep sedation. But the term general anesthesia is also used for "only" intravenous anesthesia, respiratory support may be needed but in general the patient is less sedated.
Every patient's reaction to any anesthesia can vary. Some patients get hardly any sedation (only propofol) and are zonked, slow to wake up, require supplemental oxygen and some head tilt chin lift for (hopefully) a short time. Requiring 1 to 1 nursing close observation in recovery.
Some get intubated, volatile anesthetic agents, need respiratory support during the procedure, but wake up easily, quickly, and need less post op time and observation.
So how you recover a patient from general anesthesia varies. They may need every 5 minute vitals, 1:1 nursing, supplemental oxygen, continuous monitoring and observation, etc. for at least an hour regardless of how much, what kind, of anesthesia they received.
Assisting with an acute GI bleeder is an entirely different question. They are critically ill, require GI interventions, pressure tubes in the esophagus, lavage, injection of sclerotherapy, etc., Those interventions as a nursing skill scare me more than any post op general anesthesia recovery phase.
Your anesthesiologists is your best friend and resource. When they bring you a patient ask them what type of anesthesia did they need, is there anything special you need to watch for, etc.