> I assume it reaches an equilibrium after some time
Yep definitely and in part because CO2 only makes up ~0.04% of our atmosphere. Photosynthesis processes slow when CO2 levels fall and increase when CO2 levels rise. But as well as know atmospheric CO2 levels are rapidly on the rise and is outstripping the ability of large forests to sequester it.
I assume it reaches an equilibrium after some time, and that the Amazon soil has remained the same "several meters" deep for many millions years.
But I'll admit I don't know that, and you may have a valid point. If real, this effect has to be quite small though.