It cannot be said that the energy obtained from burning carbohydrates, or any other hydrocarbon derivatives comes from oxidizing hydrogen.

There is a simplified view and a more accurate view, and neither involves oxidizing mostly hydrogen.

The simplified view, which is good enough for a qualitative explanation and for approximate quantitative computations, is that, because carbon is more electronegative than hydrogen, all the hydrogen in carbohydrates or hydrocarbons is already completely oxidized.

When those burn, only the carbon is oxidized and the hydrogen ions just move from carbon to oxygen, making water.

In this simplified view, a carbon atom from carbohydrates gives on average 4 electrons to oxygen, while a carbon atom from fatty substances or saturated hydrocarbons gives around 6 electrons to oxygen.

With the energy gained by moving an electron from carbon to oxygen of slightly more than 1 electron-volt, you can compute approximate values for the combustion heats, based on the chemical formulas.

The more accurate view is that the difference in electronegativity between hydrogen and carbon is small, so the hydrogen in carbohydrates is only partially oxidized, i.e. in each hydrogen-carbon bond the electron does not completely belong to carbon, but it belongs e.g. 60% to carbon and 40% to hydrogen.

While taking into account that the hydrogen-carbon bonds are not ionic, but they are mostly covalent, with only a small ionic component, is necessary in many contexts, for understanding burning and any other redox reactions this is not necessary and the simpler view with the completely oxidized hydrogen is more useful and it is good enough.

In any case, it is not acceptable to say that hydrogen is the one that is mostly oxidized when burning carbohydrates, because if the electrons grabbed by oxygen were attributed to hydrogen that would correspond to an energy per electron of more than 1.25 electron-volt, resulting in much higher combustion heats than obtained experimentally.

Also, the energy per atom produced by burning carbon is not slightly higher, but it is much higher than when burning hydrogen. Because hydrogen is more electropositive, the energy per electron is a little higher, but a carbon atom gives many times more electrons when oxidized (4 electrons when pure, up to 8 in compounds). Where hydrogen is better, is at energy per mass, because its atoms are much lighter.

Because hydrogen is more electropositive than carbon, non-oxidized hydrogen, i.e. pure hydrogen, produced either directly or indirectly by the internal heat of the Earth or produced by the photolysis of water done by the phototrophic living beings, e.g. plants, can spontaneously (i.e. without additional energy) reduce the carbon dioxide into organic substances, so in this sense it can be said that all life is hydrogen-powered, because it is the universal intermediate between the primary energy sources and the organic matter.

However, once the organic substances have been synthesized, the energy surplus contained in pure hydrogen has been consumed and the remaining energy, which can be obtained by burning the organic substances, to recover the water and the carbon dioxide from which they have been made, is the energy corresponding to the oxidation of the included carbon, not of the included hydrogen.