While Antarctica is not uniformly “getting cooler,” and the main process driving its contribution to sea level rise is not surface air-temperature melting. I don't know the Russian word for Bull Shit but let's say it's bullshitolia. While I agree that the evidence is fairly uniform that Antarctica has been a net contributor to sea-level rise for thousands of years, it has been dominated by West Antarctica (especially the Amundsen Sea sector: Thwaites, Pine Island, and nearby glaciers). As far as I know the dominant mechanism in the Amundsen sector is ocean-driven basal melting of floating ice shelves by relatively warm Circumpolar Deep Water. This thins the shelves, reduces buttressing, and lets grounded ice flow faster into the ocean. It does not require warm surface air temperatures over the ice sheet. Surface mass balance (snowfall minus melt/runoff) can even be positive while dynamic discharge dominates the net loss. But as far as I can tell, it has nothing to do with your imaginary anthropogenic warming.