A huge ring in the ocean, probably built of ice.

Hoists are used to dredge up nutrient rich sediment from the ocean floor, and mix them with surface water within the ring.

Grow some weedy oligotrophoc plant or algae on the surface, and collect it.

It’s then sunk down to the cold seafloor where it won’t decompose, so the carbon is captured.

You can grow the ring by using solar stills to create fresh water from salt, and since it has a higher freezing temp, just dump it on the ring after sailing to colder waters. You move around slowly via planned currents and big ol sails.

You could cheaply build many of these and they could be mostly autonomous.