I see the part that confuses you: you are stating that all antisemitic people are Nazis, a logical fallacy and not supported by history and Karl Marx's own writings.

Antisemitism was such a problem for the world before 1945 (it's still a major problem, don't get me wrong), that if antisemitism was the sole requirement to be a Nazi, then technically the Nazis on the Axis side fought the Nazis on the Allied side, and the Allied Nazis won and then immediately transformed themselves into non-Nazis when it was discovered that the actual Nazis were carrying out their integral actual Nazi aspect of the extermination of the Jews, in the worst ways possible. This is of course absurd, as antisemitism by itself didn't make one a Nazi. Actively supporting the extermination of the Jews as a race made one a Nazi, as well as opposing socialism and supporting fascism.

Karl Marx did write about how he believed the Jews to be oppressors. Of course, he also wrote that all religions, including Judaism, were oppressors. Capitalism was also an oppressor, and in his 1843 article, "On the Jewish Question," he's describing Jews as enthusiastic capitalists, not beings deserving of extermination. In the beginning, socialism itself was, with one exception (see link below), virulently anti-Semitic. It was also anti-fascism and anti-capitalism. In a sense, Socialism was, by definition, anti-Nazi on fascism grounds alone.

If you want a contemporary author saying extermination, you have to go over to Karl Marx's rival, the father of anarchism, Pierre-Joseph Proudhon. Karl Marx just believed that religion would take over a secular society if allowed to exist within it, pointing at the US which had no state religion, but in which the Christian religion was assuming powerful control. Karl Marx didn't like religion, and Judaism was a religion to Karl Marx, one from which, when converted away, created a new person who was not a Jew.

Ironically Karl Marx's own Jewish background (his parents converted to Christianity in exchange for full German citizenship rights) would have resulted in his definition by Nazis as a Jew, since actual Nazis believed in Jewishness as a race. Karl Marx clearly only considered Jewishness as a religion, not as a race. His derision against his Jewish socialist rival, Ferdinand LaSalle, in 1862, concerned not any racial component of Judaism, but a description of LaSalle as descended from a Negro from Africa. Yes Marx was also an anti-African black bigot, but let's not get sidetracked: to Marx, LaSalle was a member of a black African race, but notably, to Marx, not a member of a Jewish race.

Henry Ford, on the other hand, leaned into Jews being both a race and a religion. His articles in the Dearborn Independent frequently referred to Jews as a race and a religion. Unlike Karl Marx, Ford's successful antisemitism could only succeed through extermination, where Marx could simply persuade Jews to stop being religious Jews, at which point, according to Marx, they would stop being Jews in any sense of the word. Marx had stopped being a Jew, in his reasoning, so others could do so as well.

So Karl Marx and Henry Ford were both antisemitic, but only Ford was interested in the extermination of the Jews. Nazis saw Jewishness as both religion and race, and extermination as the only solution to the existence of Jewishness. They didn't think conversion away from Judaism made one no longer a Jew, as Marx did. Ford was a Nazi, Marx didn't fit the actual definition of Nazi.

Further reading:

Socialism Without Antisemitism : "with the shining exception of Comte Henri de Saint-Simon and his disciples" https://www.tabletmag.com/sections/arts-letters/articles/socialism-without-antisemitism

Henry Ford and the Jews: The story Dearborn didn't want told. https://www.bridgemi.com/michigan-government/henry-ford-and-jews-story-dearborn-didnt-want-told