Is this common practice for a surgeon to go home before the patient is awake?

Oh I have seen many surgeons do exactly what you describe. Even though it reflects poorly most patients don’t mention it. But they do notice little things like this. Unfortunately many plastic surgeons don’t bother to try to see things from a patient’s perspective. Probably won’t help to complain to the surgeon but you can tell all your friends and perhaps they will go elsewhere. Don’t do your surgeon the favor of telling him or her.

What you are describing is very unusual and frightening. While a stable (awake and conscious) patient may be discharged to a nurse, most certifying surgical accreditation organizations REQUIRE a physician to remain.
Find out which organization your surgeons office is certified by. Go online and read their requirements.
Glad despite this, you’re fine.

This is a very concerning management and ethics question. If you were not fully conscious from surgery then that is an issue. But why did you not call your chosen surgeon or your first responder spouse call??? Also was your surgery in a clinic setting or a private practice ?
You need answers so address with your chosen surgeon before seeking other avenues .