My server, which is old and probably somewhat power-hungry, uses ~125W. A house-sized AC unit is in the kilowatts range, that's 10x more (of course, the AC is only on for parts of the day).

If I operate that 125W computer for a year, that's ~1,000 kWh. EVs use around 0.3 kWh/mi, so running that computer for a year is the equivalent of driving an EV 3,333 miles. (Most people drive 10,000 miles a year or more.)

And if your gas gar gets 34 MPG, then it gets (via MPGe) about 1 mile per kWh. So using the 125W computer for a year is like driving a gas car 1,000 miles - and that ignores, of course, that the gas car spews pollution, while electricity can be gotten from renewables or nuclear.

So it's not like the energy usage of computing doesn't matter, but it's somewhat insignificant. Like someone else said above, it costs energy to manufacture new chips and computers too, so you might be better off just staying on old ones.