I suppose a late response is better than none! I am not very familiar with the role that Bela Kun’s legacy played in Hungary under communism, but I do know a bit about the GDR. To start, we should keep in mind that one of the most important things for a successful government is to be perceived as legitimate. This perception can be shaped in different ways, but in the modern era one of the most common ways to do so has been through nationalism. Across the Eastern Bloc, postwar communist governments also used national memory and historical figures to claim political legitimacy. Post-war communist governments invoked the memory of historical figures associated with communism to legitimate their own politics and boost their revolutionary credentials.

Marxism has always had a complicated relationship with nationalism and nation-states. Marx and Engles saw the modern nation-state as a product of capitalism that would, as Engels put it, ‘wither away’ in the transition to communism. At the same time, they also saw how useful nationalism was for advancing their political objectives. For answering this question, Lenin’s view of nationalism is incredibly important because it was a major influence on Stalin’s post-war policies. Lenin acknowledged the importance of national self-determination, but also argued that bourgeoisie's “refined nationalism” was a means by which the capitalist class could artificially divide the working class. What he advocated for was national self-determination that served class interests. If all nationalities were freed from oppressive relationships, then the workers of the world could unite freely. Eventually those distinctions would no longer matter once capitalism withered away.

To grossly oversimplify, Lenin supported nationalism as a way to unify the international working classes in opposition to the bourgeoisie and their refined nationalism. Stalin’s answer to ‘the national question’ in Eastern Europe after WWII was mostly a rehash of Lenin. To quote Georgi Dimitrov, Stalin wanted the postwar Comintern “to develop the idea of combining a healthy, properly understood nationalism with proletarian internationalism. Proletarian inter[nationalism] should be grounded in such a nationalism in the individual countries.” (Georgi Dimitrov, quoted in Jan Berends, “Nation and Empire: Dilemmas of Legitimacy During Stalinism in Poland,” 2009)

So at least in theory, Stalin advocated for an international association of autonomous, self-determined national communist parties. In practice, the situation immediately after WW2 was more complicated. Some countries had native communist parties with large local support and close ties with the Soviet Union. Others were weak and more directly dependent on Soviet backing. Others still had strong, independent communist movements that pushed back against the Soviets. However, Marxism-Leninism was the ideology of the Bloc and the nationalism pursued by every state in the region reflected that.

To get at the heart of your question, what all of this meant in practice was that, under Marxist-Leninism, figures like Rosa Luxemburg could be used as symbols of these nations’ working classes. Even though Luxemburg was a fierce critic of Bolshevism in her lifetime, SED leaders used her to give their current government a historical pedigree. Her assassination was recast as a martyring. She died fighting for us, the German workers. We are continuing her project. As Wilhelm Pieck put it in 1951 at the end of his speech at the Luxemburg-Liebkneckt March, “Rosa Luxemburg Belongs to Us!” In this way, the GDR leadership drew a line to themselves through history from Luxemburg, to Thalmann, and to themselves.

Luxemburg’s own beliefs were at odds with the GDR’s political vision, so the focus was more on Luxemburg the Martyr than Luxemburg the Intellectual. The Luxemburg-Liebkneckt March is a great example of this. Held every year by government officials and the politburo, the march went to the gravesite of Rosa Luxemburg and Karl Liebknecht. A series of speeches were held in front of the graves in which the SED leadership lauded the sacrifice of Luxemburg and Liebknecht the Martyrs and pledged to continue her struggle. So even though being accused of “Luxemburgism” was dangerous in the Stalinist GDR, those ideologies clashed in the intellectual and political space. In the public arena, the symbol of Luxemburg the Martyr was a powerful tool the SED used to present themselves as the legitimate government.

Sources:

-Georgi Dimitrov, quoted in Jan Berends, “Nation and Empire: Dilemmas of Legitimacy During Stalinism in Poland,” 2009

-Eric Weitz, "Rosa Luxemburg Belongs to Us!" German Communism and the Luxemburg Legacy," 1994

-Michal Kasprzak, “To reject or not to reject nationalism: debating Marx and Engels’ Struggle with Nationalism, 1840s-1880s,” 2012.