I cannot speak directly to the specifics of Soviet anti-Semitism as it relates to the Holocaust but I can attempt to address at least part of your question by talking about the centrality of the Great Patriotic War to later Soviet self-image. You are correct to note that the pivotal role of the Red Army in defeating the Germans, and the enormous human cost of that victory, would remain a constant refrain for the length of the USSR’s existence. Within the Soviet Union, the massive suffering of the war (a not insignificant portion of which resulted from Soviet incompetence and official cruelty, far from the hands of any German) necessitated a strong, triumphant narrative of costly but heroic victory. In later books and films, few Soviet protagonists survive their pivotal battle against the German war-machine. Among the Soviet satellite states in Eastern Europe, the Soviets would also justify their invasive reordering of post-war governments as the prerogative of a benevolent liberator, paid for in advance by Soviet blood (there is famously a clause in the 1952 Romanian constitution to precisely this effect).

The centrality of Soviet suffering to this narrative meant that it was in the Soviet government’s best interests to elide the various German atrocities committed in Eastern Europe together into a single murderous campaign perpetrated against everyone, rather than recognise the genocide of Jewish people specifically. Depictions of the extermination camps were not covered up, per se, but they were often stripped of important context when presented by Soviet authorities. It feels significant to note here that this was a departure from the treatment of anti-Semitism during the Russian Civil War when major pogroms were committed by the Whites in southern Russia and the Ukraine; Soviet propaganda was willing to recognise these crimes as specifically anti-Semitic and they remained a motif in most subsequent portrayals of the civil war.

One particularly illustrative examples of this Soviet treatment of the Great Patriotic War is the Shuhrat Abbasov film Ты не сирота (You Are Not an Orphan) from 1962. The film (supposedly based on a true story) involves an elderly Uzbek couple in Tashkent who have adopted 10 war orphans representing every major ethnic group within the USSR. Abram, the token Jewish child in this expansive Soviet family, does eventually describe the gruesome cleansing of his village by German soldiers but his story is ultimately portrayed as just one of many atrocities that have cleaved across the breadth of Soviet society; his suffering at the hands of the Germans is a mark of integration, not something that sets him apart.

Please note that I was only able to refer to Olga Gershenson’s book The Phantom Holocaust: Soviet Cinema and Jewish Catastrophe from a pdf extract so I would recommend seeking it out if you are interested further.

Why do you think it was covered or not taught? It was. But you have to realize that relative losses of soviet civilians were high af. For example, Belarus lost over 3+ million people during the War, which means that literally every third citizen of the country was killed during those 3 years (Belarus was liberated in 1944). That war was pure genocide of Slavic people so it really does make sense that much more emphasis was put towards learning about losses of who suffered the most (=Slavic soviet people), then the Holocaust.

You mind first demonstrating that the Holocaust was not taught? That's a huge claim.

The presence of Holocaust-related Soviet materials suggests the opposite.