Usually, reducing carbon dioxide comes under climate change mitigation. So, air capture of carbon dioxide for sequestration would be a mitigation effort already covered by treaty just like planting forests. It would be a big engineering undertaking, yes, but the aim is mitigation. The geoengineering ideas have more to do with changing albedo while leaving the carbon dioxide high. So, pumping sulphates into the stratosphere or putting dust in an orbit between the Earth and the Sun come in as geoengineering. Now, ocean fertilization is aimed at removing carbon dioxide but is often called geoengineering rather than mitigation so it is not cut and dry.
