If you need to remove tens of gigatons of carbon per year, you are going to need similar scales of gallium to have enough reactant operating concurrently.
Hiw do you separate it from carbon or from indium?
https://en.wikipedia.org/wiki/Gallium(III)_oxide
So we'd turn the gallium oxide back into gallium the same way we did in the first place, when we made the gallium. I'm guessing we can also come up with chemical reactions for the other two.
However, you're right that gallium production is quite low. It's a byproduct of zinc production from bauxite, and we get only a few hundred tons per year. Wikipedia doesn't say what the potential might be if we gallium were the main product.
https://en.wikipedia.org/wiki/Gallium#Production_and_availab...
Is gallium oxide dissolved in EGaIn?
electricity? Cathode and Anode?
ca 720t in 2019
We extract it from aluminum (and zinc) refinery waste because it is relatively convenient in an industrial process sense, but the amount that can be produced this way is inconsequential. The gallium in all the known aluminum ore reserves is measured in kilotons. For this application, we would need something closer to gigatons. We could produce the necessary quantities if that was the sole objective, but the cost per gram would be closer to gold which is not great when you need gigatons.