Trigger Thumb Release Surgery: What Happens in the O.R.?

Having trigger thumb release done in a few weeks. Surgeon says local anesthesia will suffice.

This is being done in a hospital surgery center, not his office (where he says he does other digits because they are less complicated).

For anyone who's had this procedure in a similar environment: Is an anesthesiologist even involved, or does the surgeon handle the numbing process himself? Is any sedation offered? How many people are assisting in the O.R.? What's the immediate post-op experience?

Thanks for any personal insights. Curious to know what to expect.