Cooling BTUs already take the coefficient of performance of the vapor-compression cycle into account. 4w of heat removed for each 1w of input power is around the max COP for an air cooled condenser, but adding an evaporative cooling tower can raise that up to ~7.

I just looked at a spec sheet for a 230V single-phase 12k BTU mini-split and the minimum circuit ampacity was 3A for the air handler and 12A for the condenser, add those together for 15A, divide by .8 is 18.75A, next size up is 20A. Minimum circuit ampacity is a formula that is (roughly) the sum of the full load amps of the motor(s) inside the piece of equipment times 1.25 to determine the conductor size required to power the equipment.

So the condensing unit likely draws ~9.5-10A max and the air handler around ~2.4A, and both will have variable speed motors that would probably only need about half of that to remove 12k BTU of heat, so ~5-6A or thereabouts should do it, which is around 1/3rd of the 16A server, or a COP of 3.