> Is it just a holdover from cold war-era terminology?

This. US and USSR were considered, rightfully, the superpowers during the cold war. "Sole superpower" simply means one has fallen, so the balance has tilt in favor of the US.

It wasn't "self proclaimed". It was globally accepted. It plays into American's patriotism but also flames anti-American in a lot of places. If you think it's just American manufactured claim you're mistaken.

In the same vein, China is considered "new superpower", also rightfully, considering how they have aggressively expanded their influence around the world.