So everything in the game (System Shock 2) works fine up until I finish basic and advanced training and I go to choose one of the three branches. I walk down one of the hallways, the little cutscene of the shuttle plays, but then it just returns to the hallway. I can walk out and trigger the cutscene again too. I don't know how to progress the game now

It's supposed to be a year later. You choose your next assignment. Don't worry, it won't go on forever.