I tend to agree with you on your classification in absolute terms. Further, I feel that moving away from a classification of "communism", will move the conversation into something that is harder to classify as a "left or right" political movement and puts it firmly in a frame of "a bid for total control, everywhere, ever". This is a frame that is maybe a bit sobering for all of us -- left, right and center.

Legacy media (at least in the U.S.) will tend to frame some of these political moves as "far leftist", while other outlets will classify public objection to them as "far right". This comes across as tailor-made to further fragment the vast majority of us being imposed-upon. It is social credit, it is public-private partnership, it is the rule of a few technocratic overlords over everyone else in an invasion of your life and your body and your mind (many would argue your soul).