There is something you are still missing; when the energy of the sun is used to create things other than heat, the worst case heat dissipated can never be more than the worst case heat that might have happened if we didn't use it at all. So whatever is created is temperature reduction. A kg of hydrogen is 33KWhrs. That is 33KWhrs of possible heat energy removed from the energy of the sun, therefore reducing temperature.
If the input energy powering all the hydrogen chain including compression is from solar, then the heat dissipated including in the compression cycle is inconsequential; what matters is that 33KWhrs of potential heat energy was removed from the energy of sun.
This is creation by definition, whereas everything done by the energy of the planet is the opposite, increasing entropy.
Knowing this, and working it through all causes and effects results in the whole business and language of renewables becoming senseless.
Carbon taxes are senseless.