Yes of course it has a limit. Nobody said that it is an infinite sink.

If you are interested in the details I can recommend J.P. Severinghaus et al., “Oxygen loss in Biosphere 2“.

I'm just surprised because somebody said that the concrete soaked up so much carbon that the trees alongside it in the biosphere were unable to grow.

That sounds like a lot of carbon. Like, a lot. I'd expect that it would have to absorb enough carbon that it could displace some amount of the volume that it would have appeared as in tree form.

Can you fit a third of a small forest into the concrete around that small forest? It seems unlikely.