I can't find a single source that definitely states it, but I'm pretty sure it's a hydrogen vent collector manifold.
This document predates the Common Centaur shown in the video, but it mentions the hydrogen vent collector manifold on page 5.9 Succeeding pages show that these (earlier) versions of the engines vented from 25 - 9 lbm/min of hydrogen during operation.
(image from same document, blue arrow annotation mine)
This frame from the video linked in the comment shows that before separation the pipe is connected to a longer pipe that goes down into the first stage.
This frame is from immediately after stage separation
There are some reddit posts about this that say it is a vent, but they are poorly sourced.