This is another huge problem of the modern construction regulations that require homes to be fully sealed. Homes used to breathe naturally with natural materials used for construction. The regulations weren’t by accident, I am sure.
Short answer is no. Your stove should be sealed and all the gasses go up the flue and chimney. If it does leak it won't just be CO2 but also CO carbon monoxide, which could put you in a very long sleep. Get a carbon monoxide alarm. But you should be fine.
I used to work in energy management / building automation 25 years ago.
These scales had values 200 ppm lower back then. With 150 out of the 200 increase happening in the last 10 years.