I have an in-person appointment to renew my passport on the 11th and have an international flight on the 12th. What is the turnaround to get the new passport? Will I get it in time to travel?

Depends on when you are traveling and how for away you live. A passport can be made same day

I had my appt the day before my flight. My flight was in the evening. I had to return on the day of my flight to pick up my passport. They told me I had to live more than 1k miles away for me to get it the same day.

I got mine the following day, given your case and since they ask for proof of travel you should get yours the same day