It was nice of the Doctor in the video linked above to talk about CO2 retention and measure it for us on a test subject. If you need that level of proof, then there it is. It is obvious from inspection however that there is nothing to the concern about CO2. The amount of volume in the space between your face and the mask is tiny compared to that of your lungs. It is quite small compared to the volume of the “piping” that leads from your nose/mouth to your lungs. Both of those volumes represent dead spaces that are already retaining some CO2 when you exhale and that CO2 does get sucked in when you inhale. All perfectly normal. Mathematically then a mask has to increase the amount of CO2 because it represents an additional reservoir of retained CO2. But it is far too small to have a significant effect on you, the measurement devices in the video don’t even register it.

The Doctor is wrong about gasses being so small that they pass right through a mask, however. Those of us who wear glasses and live in cold climates (the Doctor himself in other words!!) know from experience that a lot, perhaps most, of your exhaled breath escapes from the sides of the mask rather than passing right through it. This makes it hard to see through glasses on a cold day, they fog up from your breath! Also parachutes would not work if gasses passed right through fabrics! Fabrics offer significant resistance to the flow of gasses. But masks do not create a confined volume large enough to affect your respiratory function to any significant degree.