The Cold War involved competing blocs of military & economic peers fighting over the alignment of uninvolved nations, it isn’t just a fancy laymen word for proxy or general US - USSR remnant conflict.

This is not a world wide conflict involving superpowers with the ability to project power (hard/soft) globally, it’s at best a regional power struggle involving regional powers.

You can make a case this is the American dagger to Russia’s future aspirations beyond regional powerdom, but peers, and blocs, and cold war there is not.