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Sea ice melting doesn't change the sea levels, but Antarctica is a land mass with ice on it (and of course ice around it in the water), not just a massive chunk of floating ice.

Sea ice melting does expose bare ocean to more solar heating. Ice is a pretty good insulator, and it's also white which reflects a ton of light. Dark oceans absorb solar energy very well, there's nowhere else for it to go.

As a reference for those that aren't familiar with the Antarctic ice sheet - the average thickness is ~ 2,100m and it contains ~ 60% of all the freshwater on earth.

It's orders of magnitude thicker than most glaciers.

In Antarctica, most ice chunks are at rest on solid ground.

So, yeah, it's like adding ice cubes to a glass of water.

And the big problem is, this could be a much faster process, than the melting itself. So we might face a considerable raise of the sea levels in very short times.

Right, if very large chunks start sliding downhill.