CO2 is just an easy to measure thing but if CO2 is leaking in to the room, all the other pollutants are too. If your extraction setup was actually working properly you wouldn't notice any change in CO2 in the room.

CO2 is obviously a proxy here indeed, although it is harmful by itself.

This is not “a little CO2”. Buy or rent a sensor, go cooking without the hood set to the proper setting / a window cracked open for long enough, and you’ll be horrified.