Second Cold War

We are living in the times of remakes, so the first cold war also currently gets some renewed attention...

I think such a framing is very counterproductive because it can easily lead to self-fulfilling prophecies. I am not from the US and understand that a hegemonic power might be best served by acknowledging any possible competitors, but such positioning makes conflicts far more likely.

I see main difference is that the adversary now completely lacks any soft power. Soviet Union had a quasi-monopoly on Communism, which it promoted round the world. Although eventually it failed, it was seen as an attractive concept, promising fix to all or most evils and failures of capitalism, and was seen favourably by many people - intellectuals as well as commoners - in the West. Today's Russia completely lacks anything comparable - overall, it has nothing to offer; only reason anyone pays attention to it is the danger it presents.