Respiration and metabolism exhaust CO2 and H20 which are sourced from recent biospheric, rather than fossil, sources. That carbon is already in the biosphere, and the net carbon balance is effectively nil.

Until someone comes up with a food-synthesis process based on fossil sources (e.g., petrochemicals, limestone, or the like), this will be the case.

That's not to say that the agricultural food cycle is net thermal-forcing neutral as there are 1) fossil fuel inputs (ICE engines, generation, and Haber-Bosch nitrogen fertiliser fixation most notably), 2) other greenhouse gas emissions (notably methane from livestock), and 3) some carbon emission from ground tillage and release of carbon from topsoil. But none of those will be much affected by your respiratory rate.

The houseplants are giving me that look of disapproval.