Global estimate of CO2 from human metabolism
BiologySource
Collective human metabolism produces 2 billion metric tons of CO₂ a year, global study estimatesComments
Did they use a global average metabolic rate, or did they account for the variance between sedentary populations and those in high-activity labor? A flat average usually skews these totals.
We saw a similar attempt to quantify biological emissions a few years back, but it was dismissed because it conflated primary production with consumption. This one seems to be trying to separate the two more cleanly.
It is definitely not a closed loop once you factor in the industrial agriculture needed to feed 8 billion people. The energy spent on synthetic fertilizers alone dwarfs the actual respiration of the humans eating the crops.
The study actually notes that a significant portion of this carbon comes from the decomposition of human waste in sewage systems. That is a separate pathway from the respiratory CO2 the OP is focusing on.