Its true that Marx discusses communist society in Critique of the Gotha Programme, that is a good call out. However CotGP is not a description of communism, but a criticism of Lassalle. Marx is also very specific in the way he defines "society" and is explicit that it is a tendency of the "old materialism", which is still the dominant form of materialism as it is bourgeois materialism, to define society in a way that is static, abstract, and impractical. Marxists can't define any society in an idealist, bourgeois way, and also adhere to a revolutionary program.

Theses on Feuerbach is such an important document. Unfortunately, many Marxists do not understand it, and default to idealist conceptions of individuals and society; or at least inconsistent in how they apply a Marxist method to analysis.

From Thesis I:

The chief defect of all hitherto existing materialism... is that the thing, reality, sensuousness, is conceived only in the form of the object or of contemplation, but not as sensuous human activity, practice, not subjectively. Hence, in contradistinction to materialism, the active side was developed abstractly by idealism – which, of course, does not know real, sensuous activity as such.

It matters how we define the individual. Not just abstractly, but as a sensing, experiencing subject. Since we can't possibly imagine what those experiences will be in "communist society" we can't imagine a communist individual existing in that society.

From Thesis III:

The coincidence of the changing of circumstances and of human activity or self-changing can be conceived and rationally understood only as revolutionary practice.

This is just a really important passage, as it defines Marxist praxis. The individual in society experiences their world, thinks about it, takes action that changes it; then, by experiencing the changes, changes the self. This changed self contemplates, and takes action, so on. This process of change, the process that fuses of subject and object in the individual , is necessary to understand in order to change anything in society.

How does this relate to defining far off post socialist "communist society?" Well, communist society will be brought about through mass, continual change of this sort, the society will be defined by this revolutionary process. However, this process does not come about by achieving communist society, this process is present now and generally referred to by communists as "theory + practice." So communism isn't actually defined by a future condition but by a present condition that will continually develop into the central characteristic of individuals in communist society.

VIII:

All social life is essentially practical. All mysteries which lead theory to mysticism find their rational solution in human practice and in the comprehension of this practice.

Ideas only exist in practice. Since "communist society" can not be practiced, it does not exist. It cant define communists, it is an ideal. So what defines communism is what is practiced.

IX:

The highest point reached by contemplative materialism, that is, materialism which does not comprehend sensuousness as practical activity, is contemplation of single individuals and of civil society.

The "comprehension" of "communist society" does not even reach the level of contemplating single individuals! Only an abstract civil society. So it does not even reach the level of bourgeois materialism, it's not scientific, its pre-modern conception. It is post apocalypse, it's heaven and hell. Its fine to think this way, it is fine to daydream, but it can not be what defines us.

In the Manifesto, Marx defines communists by what we do:

The Communists, therefore, are on the one hand, practically, the most advanced and resolute section of the working-class parties of every country, that section which pushes forward all others; on the other hand, theoretically, they have over the great mass of the proletariat the advantage of clearly understanding the line of march, the conditions, and the ultimate general results of the proletarian movement.

Marx is then explicit:

The theoretical conclusions of the Communists are in no way based on ideas or principles that have been invented, or discovered, by this or that would-be universal reformer. They merely express, in general terms, actual relations springing from an existing class struggle, from a historical movement going on under our very eyes.

This is a total dismissal of the definition of communism as some future idyllic society. Right here at the beginning of part two of the manifesto. Defining communism as an idyllic future society is not the historic role of communists. Understanding existing conditions and plotting a way forward is our role.

I see too many socialists and communists more consumed by what could be than what is. And that's probably not you! I'm sure you have the correct discipline that allows you to both imagine a better world and fight for one. If imagining a better world is the impetus for actually engaging in the here and now, then that's a subjective factor that is part of the process. But emphasis matters, Lenin was known to "bend the stick". Communism is concretely not "what comes after socialism." Communism is the struggle today, not the dreams of tomorrow, and I'm tired of this other definition being what defines us.

Yes but I think points of emphasis matter. Socialism may exist in some formal ways and some informal ways, but assuming it does, for example I know that you consider China to be at least partially/mostly socialist, the task is not for a socialist nation to become a communist nation, but for a socialist nation to become a socialist international, topple imperial international capitalist totality, and continually develop mass proletarian international productive forces, etc.,

So yes it is important to delineate "communist society" vs communist movement, in that the communist/proletarian movement actually exists, as it is the embodiment of the revolutionary potential of the working class; where "communist society" does not exist, and will not exist for a very long time.

So why define communism as something that it is not? Like its fine to imagine a better world, but it isn't practical and it isn't part of communism as it is inherently prefigurative. Communists concern ourseves with what exists, and what will exist (I'm not a huge fan of predictive Marxism, but knowing where we are headed is necessary for a successful political project) not what should exist.