In a natural forest, it's true that a tiny fraction of this biomass derived from atmospheric CO2 rots incompletely on the forest floor and is turned into a small amount of carbon-rich soil, but this process is glacially slow. [1] suggests single-digit grams per square meter per year. Rotting on the seafloor may or may not be any better or worse.
Relatedly, carbon sequestration projects have biological carbon intake as one option. Instead of using industrial-scale chemical or electrical reactions to pull carbon from the atmosphere, use photosynthesis. Grow some trees, process them into ethanol and graphite, and bury the carbon-rich waste forever.
[1]: DOI:10.1007/978-3-540-92706-8_11 https://www.researchgate.net/publication/225314103_Soil_Carb...
Tree contains X Co2 => Tree dies => New tree grows in opened up space. Net Co2 = 0