There are very few Black people in Russia, most are African students or african or black American tourists.
Russia and the Soviet Union never imported slaves from Africa - Imperial Russia more or less enslaved its own population - the serfs. And the Soviets used political, and criminal, prisoners as slave labour. Russia also never had colonies in Africa, so there are no people there that can claim historic rights to a Russian passport.
But, Russia's greatest poet, Pushkin, was mixed - his great-grandfather was born in what is now Eritrea.
As to whether there are projects, yes, of course there is social lodging in Moscow, and all across the former Soviet Union. But they do not have the same reputation as the projects in the US, as they were built as apartments for everyone, doctors, workers, office workers and pilots. I stayed in a project in Ul'ianovsk for over a month - it was very safe, and the people there were all very friendly, willing to help, or just talk to the Angliskii aspirant.