“Can endoscopy be done under general anesthesia?”

Upper endoscopy and colonoscopy are usually both performed under intravenous general anesthesia. You are made unconscious for the procedure so that you remain unaware. Should anyone tell you that you will have "twilight anesthesia", that is a meaningless, undefined, garbage term not found in any anesthesia text I have ever read and should not be used. Sedation comes in three forms, conscious, moderate and deep. Conscious sedation means you are awake and can hold a conversation. Moderate sedation will be a bit "deeper" than conscious sedation where you might doze off for periods, though you remain easily arousable. Deep sedation basically borders General Anesthesia and an otherwise painful procedure like colonoscopy (if you were awake) can be done and the patient remains unaware of what is happening to them. Keep in mind that general anesthesia is a titratable level of unconsciousness. Intravenous deep sedation/general anesthesia is sufficient to perform a colonoscopy but if the patient required a surgical incision, the level of sedation/anesthesia for colonoscopy would be inadequate for surgery and requires yet a "deeper" level of anesthesia.

It certainly could, but most of the time it usually done with monitored
anesthesia care. That’s colonoscopies and esophagy-gastro-duodenoscopies.

Most endoscopies are done either with light sedation or with monitored
anesthesia care. General anesthesia is not required.

Yes, however, deep IV sedation with PROPOFOL without intubation or anesthetic gases is the usual technique. This is essentially a general anesthetic in that the patient is usually unconscious for the colonoscopy.

This is not done typically. General anesthesia is not necessary and would be excessive for most routine, average endoscopies. Deep sedation with IV medications only is the norm.