DU Bois was before the NOI, researching his philosophy its hard to say if he embraced separate but equal because he was against segregation he was after all one of the founding members of the NAACP.
"Since the founding of The Crisis, Du Bois had always written strong denunciations of racial segregation and discrimination, always springing the civil rights flagship. But over the years, seeing that the majority of white Americans were still not ready to abolish Jim Crow laws, Du Bois became tired of fighting for integration. In January 1934, Du Bois published his most controversial article of his whole career entitled “Segregation” in which he advocated voluntary segregation, abandoning all what he had been fighting for so many years.
'The thinking colored people of the United States must stop being stampeded by the word segregation. . . . The experience in the United States has been that usually when there is racial segregation, there is also racial discrimination. But the two things do not necessarily go together, and there should never be an opposition to segregation pure and simple unless that segregation does involve discrimination.388'
"What is important to understand is that Du Bois did not encourage black Americans to establish segregation but as they could not change whites' mentality on segregation, they should work more on the improvement of the unequal conditions that white authorities imposed on them...
"Du Bois tried to convince black Americans that there was nothing they could do to persuade white Americans to accept them and should now focus on their own situation to improve their economic status to increase their health and stop being “economic slaves”395 asking for integration. For Du Bois, segregation was not only necessary, but inevitable at that time:
'Assuming for the moment that the group into which you demand admission does not want you, what are you going to do about it? Can you demand that they want you? Can you make them by law or public opinion admit you when they are supreme over this same public opinion and make these laws? Manifestly, you cannot. . . . there is in the United States today no sign that this objection to the social and even civic recognition of persons of Negro blood is going to occur during the life of persons now living. . . . If you do not wish to associate with me, I am more than willing to associate with myself. Indeed, I seem it a privilege to work with and for Negroes, only asking that my hands be not tied nor my feet bobbled.396' "
https://dumas.ccsd.cnrs.fr/dumas-00925141/document
It was of course ironic that Du Bois in 1934 rook a position so similar to that he had criticized in Booker T. Washington a quarter of a century earlier. But maybe it is a mistake to look for too much consistency in Du Bois. At various times, he was a Republican, Democrat, and Socialist ; from the 1930's on, he was more or less a fellow traveler of the Communist Party, though he did not join it until shortly before his death in exile in Ghana. And his controversial articles of 1934 (which got him ousted from *The Crisis* and from the leadership of the NAACP) did not mean that he forever despaired of integration. In 1953, he wrote that "When we compare American Negroes with other groups, we are not comparing nations, nor even cultural groups; since American Negroes do not form a nation and are not likely to if their present fight for political integration succeeds."
https://books.google.com/books?id=9FNdJ8wlss8C&pg=PA239 Note that this went against the line then taken by the Communist Party that African Americans were a "nation" who in the areas they formed a majority (the so-called Black Belt of the South) had "the right of self-determination up to and including secession." (Within a few years, the CP was to abandon this position.)