https://en.wikipedia.org/wiki/Biochar production is one approach to this that is low-tech and doesn't require organism engineering. It's kinda counter intuitive that burning a rich source of carbon would keep it out of the atmosphere, but turning organic material into charcoal stabilises it and renders it inedible and insoluble, and it's really useful as a soil amendment in a lot of places, and it's very likely safe to dump in deep ocean if we ever run short of places to put it.

Farmed seaweed and algae > biochar is a very promising sequestration approach, I think.