This is a great question! I have lots to say that I can’t all fit here, but happy to answer more questions afterwards as need. Also, this is my first time answering a post here, so hopefully this is all within guidelines.

There is a very interesting Soviet comedy called Circus (1936), which is about an American circus performer who gives birth to a black child, and flees to the Soviet Union to escape the racist backlash. The final scene is this black child (held up as simba in the lion king) being passed between various ethnic groups showing demonstrating the harmony that exists between various races within the USSR.

So, what is the basis of this? The Soviet Union invited intellectuals and workers from Black America, Africa and Asia to work and study there. Many famous Marxist and anticolonial figures went through KUTV, the Communist University of the Toilers of East which trained revolutionaries, including Ho Chi Minh, Deng Xiaoping, Manabendra Nath Roy, Harry Haywood… There were also exchange programs with other friendly countries (usually Third world or recently independent from colonial rule). Woman could and did attend University. Of course, this needs to be contextualized as part of the cultural front of the Cold War being waged between capitalist and social ideologies. The Soviet Union, as Monica Popescu (2010) points out, aimed to attract intellectuals disenfranchised with capitalistic cultural production in the name of creating an alternative aesthetic. In the Post-War years, the Soviet Union trained students from Africa, Latin America, Black America, and Asia for this purpose.

To give some background information on the Soviet Union’s relationship with Black America: the Soviet Union initially seemed like a natural ally for Black America, and vice versa. While racism is hardwired into the foundations of America, the USSR had completely different founding myths. In its ideological conception as a multiethnic socialist state, it is internationally focused, with racism officially forbidden and socially taboo (regardless of the continuation of personal prejudice). It naturally seems to hold itself up a mirror to both colonialism and American racism. Maxim Matusevich writes in “Harlem Globetrotters: African-American Travelers in Stalin’s Soviet Union”, the Soviet Union saw Black visitors as natural allies, as American racism is part of its particular version of capitalist oppression.

1922 saw the Fourth Comintern Congress, which included Otto Huiswood as part of the CPUSA and famous Jamaican writer Claude McKay as a non-communist observer and participant. Additionally, this also led to Black American recruits to be trained as revolutionary organizers at the Stalin Communist University of the Toilers of the East. McKay also spoke with Trotsky on the “Negro Question”, detailed in A Long Way from Home, as well as published Negry v Amerike or Negroes in America, which served to influence Soviet engagement with Black American experiences. At the 6th International in 1926, the Comintern endorsed the Black Belt Thesis, self-determination for Black peoples in America. They also hired Black specialists, agriculturalists and engineers in the USSR that could not get jobs in America, and trained artists, filmmakers, and supported literary initiatives, being the main funder of the Afro-Asian Writers Association and permanent Bureau, the first conference of which DuBois attended in 1958 (Dubois travelled to the Soviet Union multiple times and wrote highly of it his whole life).

Langston Hughes also famously travelled to the Soviet Union. In June 1932, he came in a group of 22 young Black Americans to make a film called Black and White, about labour and race relations in the American south. Hughes describes in I Wonder as I Wander the moment the band of 22 first arrive in Moscow, the promised land of the Soviets where race prejudice was unacceptable, “a few of the young black men and women left the train to touch their hands to Soviet soil, lift the new earth in their palms, and kiss it” (98). In Moscow, the group were honored guests, staying at a hotel reserved for higher ranking party members, seeing theatre normally difficult to get tickets for unless you were a heavy industry worker, and were paid weekly salaries which (at least for Hughes), had about 100x more buying power in Russia than he was ever paid in America. When the film project fell apart the actors were offered exit visas at the time of their choosing, work in the Soviet Union, or extended travel visas. Hughes took this opportunity to travel to Soviet Central Asia, Turkmenistan, to see the part of the Soviet Union where most of the colored population lived.

In general, visiting Black Americans had far more privileges than the average Soviet citizen, and far more freedom of movement. That Hughes manages to secure a travel permit to Soviet Central Asia is itself a sign of these special privileges, given that a travel permit was valid everywhere except the Central Asian Soviet Republics (one interesting side effect of this was that writers such as Dubois or Hughes didn't easily recognize the contradictions, exclusions and violence with the with Soviet Union, but this is another discussion). In his travelogue A Negro looks at Soviet Central Asia Hughes will comment extensively on the cotton production near Tashkent (modern day capital of Uzbekistan). The Soviet Union had invited Black agricultural specialists and engineers, a team that worked under specialist and KUTVA student (the University of the Toiler’s of the East), Oliver Golden. Golden had been unable to find specialist work in America, but the Soviet Union sought out skilled Black American labour. Golden was paid 700 US dollars a month. If anyone remembers the Soviet Union’s relationship to its farmers and peasants around this time, this is an enormous sum. It is also an enormously different experience to the ambivalent and often coercive relationship between agricultural producers and the Soviet state.

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I’ve written tangentially about this topic in this other answer, which was about race and ethnicity in the USSR more generally and have borrowed some sentences and phrasing from myself to use in this one. This is within the plagiarism guidelines of the sub, but I want to state it explicitly.

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So, the direct, not-beating-around-the-bush answers are: pretty normal but sometimes really not; pretty well but sometimes really not; not in your personal life but possibly in the media; no; legally nothing but socially something; no, or at least not because they were black; not applicable. So as you can see, we’re going to have to beat around the bush a little.

Foreign students were probably at their most visible during the Khrushchev Thaw and the late USSR, but their history actually extends throughout the Soviet Union. Lenin’s contributions to the theory of Marxism famously include his explanation of imperialism and colonialism as "the highest stage of capitalism", so after the success of the October Revolution, he and other Bolsheviks intended to transform the RSFSR and later the USSR into the vanguard of not just socialist revolution, but also racial equality and decolonization. In the late 1920s, this would take more concrete form with the policy of korenizatsiya, which I wrote about here.

But even before then, the ideal of international cooperation found expression in the Communist University of the Toilers of the East, or in its Russian initials, KUTV. KUTV was founded in 1921, under Lenin. It was first intended to be a technical school sending qualified engineers out to modernize their home republics, but about a third of the student body was from outside the USSR, including students from multiple African countries. So what was life at KUTV, and in Moscow more generally in the 1920s, like for African students? Well, sadly, I don’t think anyone has actually produced a study of their perspectives. But we can say a few things about the environment they would have found themselves in. Moscow was even more predominantly Russian then than now, which may have made feelings of otherness and isolation even worse, but foreign students would have lived in dormitories administered by their universities, and since KUTV explicitly admitted minoritized ethnicities, Africans were at least able to share their plight with their co-students.

Although he was neither African nor a student, Claude McKay’s case is one of the best examples we have of what a Black man thought of the Soviet Union’s claim to racial equality in the 1920s. The other answers have already discussed McKay’s actual experiences in the USSR, what he did and who he talked to, but we can go a little more into what he actually thought about those experiences. And oh boy, did he gush about them. He even described it as a "magic pilgrimage", he was so impressed; there was no housing segregation, no being forced to sit at the back of the bus, no lynching. Part of that is because visitors of McKay’s international stature were few, and they all got rooms at the best hotels, enthusiastic gala receptions, and were explicitly to be protected by the police.

But even for less famous guests, things compared favorably to the US, and especially the Jim Crow South. Even for those not booked hotels by the state, housing segregation was never even close to policy. Even for your average unknown Black visitor, Russians would often "willingly [vacate] their seats on public transport to accommodate a 'Negro comrade'" (Matusevich 2008, 61f). By no means were the majority of Black visitors and migrants celebrities, though. Engineers, agricultural experts from Tuskegee, and even laborers and mail carriers could move to the USSR and often do better than they would have back in the Depression-era US. (For more on the USSR’s insulation from the Depression, I recommend this post by u/kieslowskifan.) They often remained for years, as well, so "visitors" is a bit of a misnomer in many cases.

This does have a double edge to it, though. Africans, and Black people in general, were novelties in the USSR. Even if you weren’t Claude McKay, there was a fair chance you were there as an honored guest, and if you weren’t, that honor rubbed off on you by virtue of your rarity, and your status as a symbol of international fellowship, all the same. So Russian politeness on public transport should definitely be seen as genuine, but it was also because of that novelty, and because of a sense of paternalism. (Anecdote time: When I lived in Moscow, I, a young white male student, basically never sat down on the Metro, because even when there was a seat open, odds were I would just end up offering it to a woman older than me at the next station. Giving up your seat is always a sign of respect, but sometimes it also indicates socially constructed assumptions of weakness.)

So I don’t believe we should consider anti-Black or anti-African racism virulent in the pre-WW2 period, because again the people who would have experienced it first-hand rarely mention instances of it. But it was by no means a post-racial utopia either. And as Soviet policy developed, more African students came to the USSR, and their novelty wore off, the rose-colored glasses slipped as well. Later in Stalin’s life, the USSR became more isolationist and inwardly-focused, so things remained broadly the same, if even less eventful, for Africans and Black Americans in the USSR. KUTV was closed and foreign student hosting was cancelled in the late 1930s, as Stalinist paranoia reached its peak, and no American celebrities would be quite as vaunted by the Soviet press after the mid 1930s — although Langston Hughes’ and Paul Robeson’s Soviet experiences in the early 1930s do mark a last, highest hurrah for Soviet adulation of Black western cultural figures.

The second major moment in this history comes after Stalin’s death, in the Khrushchev Thaw. Khrushchev’s reforms and liberalizations were accompanied by a turn outwards and a renewed interest in Africa and Asia, for their geopolitical significance but also for their rhetorical value. That meant a propaganda push in those "Third-World" nations, but also an increase in the number of students who would be invited to the USSR. Ghana’s independence in 1957 was the beginning, though perhaps not the spark, of a massive wave of decolonization in sub-Saharan Africa and of a blossoming of African socialist movements. It also coincided with the 1957 World Festival of Youth and Students, which inaugurated in the Soviet consciousness a new tone for its relations with Africa. As more nations gained independence, the USSR offered educational opportunities to students from more and more of them. There were students from ten African countries in 1958; by 1968, there were students from forty-six (Guillory, 273). Exactly how cynically realpolitik this move was is one of those issues that historians will probably never solve definitively — I tend to think it had origins in an earnest desire to help, but you can make a strong case otherwise too — but it was certainly paternalistic in its language, claiming to "help the downtrodden," among other clichés (Guillory, 273).

The paternalism filtered through to the students in question, although it didn’t exactly rule their lives either. Students from non-Russian backgrounds, including Africans, were given a certain amount of extracurricular help such as tutoring or special language lessons, which certainly did help them academically, especially considering many didn’t speak perfect Russian. The fact that the help was portrayed rhetorically as a "benevolent gesture" definitely created a "patronizing [...] 'white man's burden'" atmosphere for the African students who received it (Walke, 305). The frequency with which Soviet citizens, official and unofficial alike, asserted the superiority of the USSR over the West also contributed to a feeling that everything was being done for show, to prove a point. The Soviet citizens in question may have honestly believed they were combating imperialism, but it relied on the same unspoken assumptions of African backwardness, with the difference being an assertion that only the USSR was truly committed to ameliorating them.

Students were not really treated as propaganda pieces, at least not in their own lives and not as individuals. Propaganda about international brotherhood found plenty of expression in news media and in the form of party-organized festivals such as Komsomol Congresses, where everybody was supposed to be on display and were only elevated above that baseline level of on-display-ness if they’d been specifically selected to take part in a dance performance or something of the like. So there was no need to use individuals for that purpose. But exams sometimes seemed awfully easy, lessons comically doctrinaire, professors either much too accommodating or oddly strict on the smallest failures; that they would be blamed if a foreign student failed goes a long way to explaining both their willingness to help and their tendency to snap. So paternalism was not something African students could fail to see, but it was more of an undercurrent than a sustained wave.

What a terrific post!