Why? carbon goes into the seaweed, seaweed gets turned into bioplastic which contains that carbon. Bioplastic is used and then discarded into a composter. Composter degrades the bioplastic, the carbon (and other nutrients) are in the compost that is created?

Composting does not sequester carbon. Yes it would replace mineral carbon, but that is not what sequester means.

Is it easier to capture carbon from decomposition than directly from the atmosphere? If so that could be how this works.

I get your point, "biodegradable" is not necessarily indicating the end state, but I think it's generally a better idea than using previously sequestered carbon like oil (depending on the energy needed to produce useful goods, and the source of that energy). As a related example, anything made of wood is biodegradable, but if you then burn it, you're not really capturing any net carbon, although you are sequestering it for a period of time.

Isn’t this more a question of how long the carbon is “sequestered” before it mostly biodegrades?

How quickly does the seaweed biodegrade? Over weeks, years?