As our planet gets greener, plants are slowing global warming

[Syne]

So the ecosystem has natural means of reestablishing balance

The paper referenced in the OP speaks of an effect - you speak of a balance  - these are not the same thing. I assume by balance you mean that the amount of CO2 removed is equal to the amount of CO2 added such that over the course of a year the amount of CO2 in the atmosphere does not increase. I am looking for evidence of that balance being achieved.

I said "reestablishing balance", not just balance. Any effect that lowers CO2 is one that works toward reestablishing a balance. No one said anything was currently achieved.