You're right, there seems to be iron rich deep sea currents in some places that could be good opportunities for upwelling, especially if you had a carbon neutral way to do it.
There is also emerging technology for nitrogen fixing that could work - Electrocatalytic Nitrogen Reduction.
All this being said, if the goal is carbon sequestration building a viable business is going to be next to impossible.
The easiest way would be to use your renewable energy to pull bicarbonate out of the ocean directly with electrolysis, reverse-osmosis, whatever magic tech the wizards in MIT are cooking up.
Only then you've got the problem of what to do with it all once you've got it on hand.
Carbon sequestration is merely a side effect, the main goal is to have a wavebreaker and a park and a place to grow fruits, for a floating city.
To bring nutrient rich water up and to generate energy in the process temperature difference between surface and deep water can be used [1]. So if this kind of tree is created, living on open sea can become cheaper and more pleasant than even living on a beach.
There is also emerging technology for nitrogen fixing that could work - Electrocatalytic Nitrogen Reduction.
All this being said, if the goal is carbon sequestration building a viable business is going to be next to impossible.
The easiest way would be to use your renewable energy to pull bicarbonate out of the ocean directly with electrolysis, reverse-osmosis, whatever magic tech the wizards in MIT are cooking up.
Only then you've got the problem of what to do with it all once you've got it on hand.
[1] https://www.nature.com/articles/s41467-023-36992-1