It’s a command center of a complicated operation, nobody cares if someone has a camera issue on a side goal, it’s all about situation. I vote the booster was lost, and it was not worth using more bandwidth on it.

The quote from the video is: "We lost the center core."

For those like me unfamiliar with the terminology used in this context, is this wording reserved for situations where the rocket is destroyed or could it also mean they lost contact/video feed with the center core?

They normally call out "LOS" or "loss of signal" when they lose a video (or any other kind of) feed, but I have heard it on other streams that they say something like "We lost stage 1... signal/camera feed".