I’ve had three surgeries under GA and went home the same day for two of them. I’ve also had two colonoscopies, rhinoplasty, and a D&C, all of which were done under lighter anesthesia, and I can’t tell the difference between the GA and the lighter stuff. In my experience, regardless of how heavily they are sedating you, you go out really fast, are prone to memory blackouts in the hours after you wake up, and are pretty functional right away, just very tired.
I wouldn’t recommend driving (in fact I suspect you won’t be released unless the hospital/clinic verifies that you have someone to get you home), but I have walked home or taken public transit by myself shortly after surgery.
The medicines/procedures used have definitely improved over the years, so if you are relying on old stories, you probably shouldn’t assume you are subject to a similar experience. It used to be that people were subject to a noticeable period of incoherence/confusion upon waking; my doctor friend told me that she had heard some pretty amazing comments from patients who were still woozy and didn’t know what they were saying. But for my most recent procedures, the doctors told me that the latest anesthetic is pretty good, and you snap back to full consciousness pretty quickly, so no worries over making an ass of yourself while in a half-drugged condition.