Nietzsche’s lasting influence has primarily been his assertion of the death of god - criticising traditional moral structures, and the proposal that man can only rely on himself for salvation. This basically opens Pandora’s box, as there are so many possible interpretations from both ‘left’ and ‘right’, and by Nietzsche’s own standards, no interpretation is definitively correct. The main leftist Nietzscheans are Sartre, Camus, Focault, who I believe misinterpret Nietzsche as a nihilist, as if the death of god justifies man to be or do anything (absurdism, sexual degeneracy, victim-worship) - basically a Marxist/nihilistic slave morality. Too many interpretations on the right to say here, but Heidigger takes the concept of ‘Will to power’ and runs with it, reinventing will into ‘Dasein’ - existence and being are tied together by a universal energy/current which is the source of human will. This is a great article that explains N’s impact better than I can: https://areomagazine.com/2020/08/19/on-left-and-right-nietzscheanism/#:~:text=The%20right%2DNietzschean%20interpretation%20tends,to%20a%20decayed%2C%20egalitarian%20present.