Just be careful with specific technical definitions of things.

A capacitance of 710 uF just means that if you charge up the earth's surface with 710 uC of charge then dragging an electron from infinity onto earth will impart 1 eV of energy to it. (One volt of potential from infinity)

That's not what you are doing when you are analyzing some circuit grounded to earth. If you throw a bucket of salt water onto some transformer or something and short some high voltage line to ground then you are actually just redistributing electrons and ions around within the earth's surface and in the atmosphere. You can do this "infinitely" because those electrons eventually will go back to / come back from wherever this high voltage is originating from.

However as a caveat there genuinely is a lot of voltage created from all these charge imbalances and therefore the capacitences of these systems is indeed quite small just like theoretical equations predict. Like the atmosphere has something like a few hundred volts per meter potential if you are going straight up and as I understand this huge potential is created by a relatively small numner of imbalanced ions in the atmosphere. Also if you actually fault a grounding connection in practice then you do get a large potentially dangerous amount of voltage on the soil.

Maybe this is wrong, but as I understand it the more correct model would be having a resistor connected to a small capacitor which is the earth, but this small capacitor has a discharge resistor that eventually drains all the voltage away as the charges return to the source.