This seems like an electrochemical process. A simple demonstration I used to do when teaching chemistry was to put an iron (Fe) nail into a silver nitrate solution (AgNO3). Immediately, you would see silver deposited. The Ag and Fe swapped, producing Ag and FeNO3.

Similarly, in this paper, electrochemical activity is converting CO2 and Ga into C and gallium oxide. The C and the Ga swap. The reaction is spontaneous. No need to add any energy for this reaction to occur; it proceeds because the products are more stable than the reactants.

Where is extra energy required in the process? Energy is required to melt the Ga to about 200C. Energy is also required to reverse the oxidation, i.e. to replenish the Ga. A supplement to the article explains that this was done by electrolysis: gallium oxide was converted into Ga and oxygen [0]. I guess, that they figure to use solar energy to generate the needed electricity.

I'm with you as regards the unfeasibility cost-wise. What they are obviously doing is exploring uses of low melting-point metals [1], hoping to strike it lucky with one of their projects. And, yes, these guys have obviously got their publicity department working overtime in order to generate more grants.

In a recent video, the co-lead scientist, Associate Professor Torben Daeneke [1], explains his various projects.

-- 13 min: The melting point temperatures of the metal/alloys they are working with.

-- 61 min: Their latest work , CO2 to coal.

And here's a video showing the bubbling of CO2 through Ga-In (gallium-indium) alloy to form carbon [2].

[0] https://www.rsc.org/suppdata/d1/ee/d1ee03283f/d1ee03283f1.pd...

[1] https://www.youtube.com/watch?v=fvsON7af2J0 Jan 2022

[2] https://www.linkedin.com/feed/update/urn%3Ali%3Aactivity%3A6...