I know that a greenhouse is not air tight so I imagine it breathes somewhat and exchanges gas with the outside. However, I also assume that it’s going to use up the co2 in it for plant growth. How does it not run out? I think you could vent it, but then wouldn’t that cool it off and thus defeat the purpose of a greenhouse? All my web searches either give climate change facts or co2 supplementation by farmers.


Usually both, in my experience.
You’ll have fans for plants that firm up stems and stuff, in addition to helping with transpiration.
Then you’ll have fans or passive vents near the highest point that move air outside, usually for the sake of venting excess heat and humidity. If you live somewhere cold, these probably stay closed through colder times and are active/open only during the height of summer (these are often the passive vents). If you live somewhere warm, it’ll probably always be active fan-driven, and usually running.
A lot of people have their ventilation system hooked to climate control sensors, so it only engages when it crosses a certain threshold.