This graph is important
It’s based on the writings of professor Cheng Enfu, President of the Academy of Marxism at the Chinese Academy of Social Sciences (CASS) and Director of the Academic Division of Marxist Studies of CASS.
Socialism and communism are not one and done processes. They are gradual changes, both Marx and Lenin have addressed this extensively. We can’t just instantly press the big communism button unfortunately.
Here’s a paper that goes way more in depth on the professor’s definitions: https://guilfordjournals.com/doi/pdf/10.1521/siso.2022.86.2.159
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Communism isn’t a centrally managed economy. That’s not the definition of communism. The USSR/CCCP never achieved communism, but were stuck at the transitional/intermediate state of socialism. Make of that what you will.
Public ownership doesn’t have to mean central ownership. There is such a thing as local government.