The uptake of carbon by the ocean is strongly dependent on temperature. As you warm, the efficiency of uptake becomes weaker.
If you look at outgassing, the single most effective means of outgassing is volcanic emission. On very long timescales, the carbon from the ocean went into the sediments. The sediments were eventually subducted under continental plates through tectonic processes. The carbon would eventually go back into the atmosphere again via volcanic emissions. This a very long timescale carbon cycle (many millions of years).
Nowadays, the concern is not so much getting it out. Rather, the oceanic buffer is reducing its efficiency. As we put more CO2 into the atmosphere, the ocean is less and less effective in absorbing what exists already. There are other processes: if you get CO2 enriched water and bring it to the surface you can outgas instead of uptake. But there is an awful lot of deep ocean that can still take up carbon. The key is really that the surface ocean becomes less effective as it warms, which means more CO2 in the atmosphere.
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