In a general anesthesia you can't breath on your own so they stick a tube in your mouth. And it needs a special doctor (anesthesiologist) to perform the general anesthesia.
There was no anestesist (extra doc) present in the procedure, so I assumed it was no general anesthesia. But I dont know. Was it?
I don’t know the distinction between that and “general” anesthesia (they called this general), but I know there are different levels (and there was no need for breathing assistance at that level).
General anesthesia is a big deal both for the patient and for the doctors/hospital.
As an added bonus the doctor can show you anything they find on the screen and answer questions.
It wouldn't have occurred to me at all to ask them to put me under if there's a next time. And according to my SO, I'm rather pain intolerant.
If you're doing a biopsy I can imagine it's something else.