Your example incorrectly assumes the entire solar constant went toward carbon sequestration and this is obviously not the case.
The overall energy efficiency of the natural photosynthesis to sequestered carbon process is not inherently more efficient than man-made alternatives. The efficiency of the PV cell is just one small factor.
A much more accurate way to calculate sequestration potentials is to measure their energy cost and multiply by available energy.
It's just a Fermi estimate. Feel free to multiply/divide by ten (or even 100!) in either direction. The main point is that we're not going to carbon capture our way out of this--at least not with anything resembling modern technology.
But your estimate is demonstrably off by at least a factor of ten thousand.
The thrust of this paper is that it takes 90 tons of ancient biomass to result in 1 gallon of gasoline. This is a reduction of 30,000 to 1. This is the opposite of an efficient system. The vast majority of solar input and related carbon captured from the atmosphere by ancient plant matter is not being utilized by modern fossil fuel systems.
The point of this paper is that the ancient photosynthesis to fossil fuels process is incredibly inefficient. The "400 years" isn't indicative of the energy we're consuming today -- it's indicative of the extremely low percentage of solar energy that ends up captured inside fossil fuels.
We absolutely can carbon capture our way out of this. Again, you can do some pretty basic math on known sequestration techniques to disprove your conclusion.
I'd put my money on directly modulating incoming solar radiation instead
From the first time I saw the animations of the planned Starlink fleet, I started wondering if one could use a satelite fleet to manage incoming solar radiation.
The overall energy efficiency of the natural photosynthesis to sequestered carbon process is not inherently more efficient than man-made alternatives. The efficiency of the PV cell is just one small factor.
A much more accurate way to calculate sequestration potentials is to measure their energy cost and multiply by available energy.