Hey sorry for the delay in response. I got caught up with life but now am sick in bed with a cold so i have time to respond to this.

The basic premise I’m working from is that both Marxism and anarchism are extremely broad political traditions that have evolved through numerous internal developments, reinterpretations, and hybridizations over more than a century. Because of that long intellectual history, I think it becomes increasingly difficult to draw rigid boundaries between the two traditions. They have generated many overlapping currents, shared theoretical concerns, and moments of mutual influence. For that reason, I’m somewhat hesitant to treat Marxism primarily through the lens of dominant political parties or official tendencies (for example, Marxism-Leninism in communist parties). That approach tends to privilege institutional power over intellectual development. When discussing Marxism as a theoretical tradition rather than as a party ideology, the landscape in my opinion becomes much more diverse.

i can't state what is the most common tendency globally or refute what "most people in parties believe" What I do know, however, is that there is substantial literature both historical and theoretical that examines how Marxist and anarchist ideas intersect and inform each other. That show how these traditions have developed alongside eachother, indeed sometimes historically in opposition about also many times not.

There are terms that have shown the overlap: Anarcho communism, libertarian socialism, council communism, strands of post situationist or tiqqunist inflected theories. Each of these traditions draws on Marxist critiques of political economy while simultaneously adopting anarchist critiques of hierarchy modalities.

A book that illustrates this historical interweaving beautifully is Communal Luxury by Kristin Ross, which explores the intellectual and political legacy of the Paris Commune. Ross shows how early revolutionary movements that later became identified with either Marxism or anarchism were deeply intertwined at their origin. Another is Wayne Price, such as his book "the value of Radical theory: An anarchist introduction to Marx's critique of political economy". And theres also a lot of his stuff here https://theanarchistlibrary.org/category/author/wayne-price

There's also a lot of historical analysis that point out structural similarities between anarchist and marxist revolutionary organizing. For instance, this test by Rene Riesel on councilist organization discuss parallels between the CNT-FAI in Spain and the KAPD-AAUD in Germany that suggests how despite ideological disputes their organizational models and aspirations had major similarities.

anarchism and marxism, from a "party like" perspective, treats things and defines the antagonism as perminent, when historically it was actually much more complicated. There were of course major conflicts, but there were also many shared goals, overlapping analyses of capitalism and practical collaborations. Speaking of the non-english thing, some of the best examples of it are in non english/ global south countries! South america for isntance.

Maybe i'm not answering your question/comment correctly. If so my apologies.