"confidence" doesn't have to be an emotional state. It's essentially just another word for "probability" here - any model's confidence of X is the probability it yields for X. Isn't this common terminology?
Personally, until recently I can only recall people saying things along the lines of “applying the model indicates that we can state this fact about the data with this much confidence”, never “the model has this much confidence” in some truth statement, especially one independent of its training data.