Okay, baking soda is sodium bicarbonate (Na^+ HCO3^-), so the addition
of that will increase KH as bicarbonate concentration has increased.
CO2 dissolves in water to form hydrogen bicarbonate (bicarbonic acid):

CO2 + H2O --- H^+ HCO3^-

Okay so you mean H2CO3.
Not the bicarbonate ion -HCO3?

I think there's some confusion there on those two terms.

Adding CO2(acid) will never form the KH (-HCO3), a buffer in this
case.
The above has _no buffer_ to start with, you assume pure water. A tiny
tiny amount will form H2CO3 but about 1:400 will be CO2 so most folks
ignore the H2CO3.

But H2CO3 is not KH. There is no alkalinity in pure water. There is no
acid base buffering system either.

Dissolving CO2 in water increases bicarbonate concentration, so why
would it not increase KH?

It does not change the bicarbonate at all.

I leave a glass of water out, it has a KH of 5. I add CO2 to it, it
still has a KH of 5. You are welcomed to try this yourself.

The total carbon has increased when you add the gas and the pH will
drop, but the KH is the same, it does not gas off or evaporate. The
gas will and the buffered solution will equilibrate and return to
starting pH if you stop adding the CO2 gas.

Regards,
Tom Barr