Meaning of "the piano cut holes into the very piece of cardboard ... drink of the black milk of dawn"?

Hello everyone. I am reading a novel, and I came across this expression. Could you please let me know its meaning?

Without hesitating or even waiting for our response, he proceeded to play the Bach-Siloti a second time.

Deftness and dexterity, something so easy, lambent, and yet ever so contemplative in the face of what lay in store for the likes of Czernowicz, who was, so many, many decades later, still speaking to God. I kept thinking of his playing this piece as the piano cut holes into the very piece of cardboard in front of us—how could he not have known that in a few years he’d drink of the black milk of dawn? The more I listened, the more it seemed to become more about him than about Siloti, more about Jews like Max who outlived the Holocaust but would never live out its sentence, more about the fugue of death than about Bach’s prelude and fugue.

- André Aciman, Eight White Nights, Third Night

This is a novel published in the United States of America in 2010. This novel is narrated by the nameless male protagonist who meets Clara at a Christmas party in Manhattan. Two days after the party, Clara came to the protagonist's house in the morning and drove him to her best friend's house named Max, who is the grandfather of her ex-boyfriend and childhood friend Inky. At his house, they are all listening to the Bach-Siloti that Max played.

In this part, I wonder what the underlined expressions might mean.

What would it mean that the piano cut holes into the cardboard...? And what would it mean that he would drink from (=of) the black milk of dawn...? I feel that these expressions might be connected because they are in the same sentence, but I am not sure.

Thank you very much for your help.