I think there's a bit of a disconnect here. The Anarchist conception of Communism and the Marxist conception are similar sounding, but fundamentally entirely different. This is due to Anarchists seeking to abolish hierarchy, while Marxists seek to abolish class. What does that look like?

For Anarchists, this path generally takes the form of a horizontalist network of communes, or other such unit. Communes have equal ownership within themselves, and trade with other communes via systems of Mutual Aid. The general Marxist critique is that this turns everyone into Petite Bourgeoisie, all interested in the success of their own commune over the entire system the way a Capitalist is more interested in their own profits than those in their supply chain, even if they depend on each other. This can lead to inefficiency and a resurgence of Capitalism.

For Marxists, this path takes the form of collectivizing all industry into full public ownership and planning in a global republic. This requires administration, government, etc, though many of these functions become less necessary when moving beyond class society. The Anarchist critique is that this retains hierarchy.

So, in a way, Marxism is the only path to what Marxists describe as Communism, and is absolutely not a path to Anarchism.