Most people knows that the ocean overall is a carbon sink, but a big part of the sink is due to chemical equilibrium (via dissolution) with the atmosphere (for ref: https://link.springer.com/article/10.1007/s10021-005-0036-3). Not all the (chemically) dissolved CO2 is consumed by primary producers in the ocean (simple deduction from ocean acidification).
In terrestrial ecosystems, we have a term called net ecosystem production (NEP) which is defined as gross primary production minus the total (autotrophic + heterotrophic) respiration in an ecosystem (generally a meaningful timeframe should be at least on an annual basis). I wonder is there any research done regarding the NEP of the ocean? (I am sure there are some out there but I cannot find a conclusive summary of the entire ocean or at least a big part of the ocean). I am assuming this would be harder to measure than terrestrial ecosystems considering how big the ocean is and the big confounding factor of physicochemical processes in the ocean.
Edit: I found somebody trying to answer the same question 20 years ago (Del Giorgio, P. A., & Duarte, C. M. (2002). Respiration in the open ocean. Nature, 420(6914), 379). But in it, it said the answer remained uncertain. I am assuming there would be advances since then.