The question of whether communism is purely economic is a tricky one. On one hand, the theory is mainly economic and as communists we understand that the root of all politics is economics, because we need to know how the people are going to eat and also how resources are going to be distributed in our society. However, there is something strange going on where unsavory characters are advocating communist economic systems while also upholding rightist and first-worldist ideas that are used to reinforce inequality and the continuation of capitalism. At best they completely misunderstand how such a system would affect society, and at worst they want to create a form of socialism only for the people who are already relatively privileged in society and exclude those who they are prejudiced against.
While communism is technically purely economic, the ideas of socialism create an environment that makes oppression of people by the bourgeoisie impossible. If we understand the United States to be a plutocracy and playground for the world’s bourgeoisie and also a settler-colonial nation that continues to exist at the expense of the indigenous people, then we cannot justify a socialist project that continues the existence of America in its current form or even a recognizable form. There is a reason that those who seek to overthrow capitalism are those who have the most to gain from its destruction. These are ethnic minorities, discriminated people, or those who are not allowed to live peacefully or make a living under the current organization of society. Those who are homeless or those who struggle are the ones who will truly want to dismantle the system and create something equal. The relatively privileged classes of society such as White Americans do have a lot to gain by overthrowing the bourgeois regime and establishing democratic control of the economy, but this would require allowing minorities to have a voice as well which requires them to see beyond the short-term comforts granted to them by colonial privilege and white supremacy.
So while communism on paper is purely economic, the philosophy is anti-imperialist which would make it incompatible with any pro-America sentiment and would require decolonization in Turtle Island and an end to the imperialist wars that liberal politicians continue to call for. It is also dialectical and would require the people to look deeper than blaming the oppressed peoples for their own problems, instead looking to the material conditions which drive human behavior and the circumstances that lead to society becoming the way it is. For people who have spent life under capitalist oppression and developed survivorship biases, just world fallacies and other ideas to help them cope with the brutality they lived through, this takes some mental effort. Even that is assuming they don’t participate in even more overtly reactionary politics that we see in The US, where politicians openly advocate cutting welfare and taking food and housing away from working class families and the media actively cultivates prejudices against ethnic minorities.
Communism may be based in economics, but it is a theory that makes current systems of oppression substantially more difficult if not impossible to maintain, at least on an economic level. It is not an ideology that is meant to appease reactionaries based on their conspiracies of ethnic replacement or their desire to force religion onto oppressed peoples. Communism is a system by and for the working class, and the working class includes those who are discriminated against and often looked down upon by society. Any form of socialism that seeks to exclude any segment of the working class or grant extra privilege to a white working class is reactionary, revisionist and non-dialectical.
“In the social production which men carry on they enter into definite relations that are indispensable and independent of their will; these relations of production correspond to a definite stage of development of the material forces of production. The totality of these relations of production constitutes the economic structure of society. The real foundation on which legal and political superstructures arise and to which definite forms of social consciousness correspond. The mode of production of material life determines the general character of the social, political, and spiritual processes of life”
~ Karl Marx
As for yourself, I think you answered your own question in the third paragraph.
This is the answer I came to give. Communism is an economic mode of production, but how the economy operates is also what defines almost every other aspect of society.
On the other hand, Dialectical Materialism is a tool we can use to analyze history, current events, societal structures and make predictions. It’s through this tool that we recognize the relations between economic production and society at large, as well as the flaws of capitalism.
Marxism is firstly a critique of capitalism, and secondly (but equally important) the solution to capitalism.