No, but it did have a tendency of omitting/censoring[1] the fact that it was primarily directed at Jews and Romani, as highlighted by Yevtushenko in his poem.
[1] https://en.wikipedia.org/wiki/Babi_Yar_memorials#Commemorati...
[1] https://en.wikipedia.org/wiki/Babi_Yar_memorials#Commemorati...
On top of the already complex ideological balancing act involved in managing so many distinctive national and ethnic identities, particularly along the periphery, there was the strong official Marxist internationalism, the idea of friendship among the proletariat of all nations, and of the Soviet Union as a superlative embodiment of this, etc.
With such ideological/rhetorical objectives in mind, whatever you may think of them, it is easy to see why it would be a problem to give any particular people a sense of preeminent victimhood or confer unto them some special recognition. It can lead to enhanced claims for special status or compensation from those people, as well as animate the grievances of other ethnicities who were the victims of Stalinist policies such as forced mass resettlement, or who lost disproportionate numbers in the war, or succumbed to famines and collectivisation of agriculture, etc. Besides that, the USSR lost an estimated 27 million soldiers and civilians fighting the Germans--people of all sorts of ethnicities, but of course to no small extent Russian-Slavic. A self-interested government would not wish to antagonise veterans or grieving families by creating the perception that the mantle of victimhood was being somehow disproportionately alloted to a particular group.
So, there was generally a political reluctance to cast any particular spotlight on the distinctive plight of Jews in WWII. Doubtless, some amount of inertial anti-Semitism and a suspicious view of Jews played a role too.
From the same Wikipedia page: "An official memorial to Soviet citizens shot at Babi Yar was erected in 1976." Yevtushenko starts with an incredulous observation that there is no memorial at all, as of 1961. Your comment hints at a possible reason: it may be difficult to commemorate this specific site if one is unwilling to mention the Jews. It is imaginable that had a memorial existed--in any form--the poem may not have been written, but its lack had caused the poet to search for reasons.
As to your larger point, entirely fair.
It took until 1991 for a memorial explicitly mentioning Jews to appear.
https://en.wikipedia.org/wiki/Russification#Under_the_Soviet...
You seem like a Soviet apologist
Same in the GDR by the way. Memorials in concentration camps often highlight anti-fascist fighters who died there - no mention of Jews, Roma or Homosexuals.
From a US passport: "Nationality: United States of America"
From an Australian passport: "Nationality: Australian"
I have not seen an EU passport, but as far as I know EU does not claim ideological erasure of any national identity in favour of some ideal "European".
[Edit: No accusation of racism had been made, whether I believe it to exist or not. The point is that it is difficult to claim ethnic identity does not exist, while explicitly highlighting it at every opportunity. The two countries I single out above make a point of being "melting pots", and are much more consistent in applying that.]
Country Code: GBR Nationality: British Citizen
Along with the town of birth, which is not enough to get any more information about ethnicity than you could from the name and picture.