New Old World Order? – Can state-capitalist China inherit the United States’ position as global hegemon?

Can? Absolutely, it is without question theoretically possible. Will they? Probably not, they're too focused on Taiwan and historical redress, and not enough on soft power projection through the world.

Nobody really owes China enough favors.

And while they're staring at a mountainous, chunky island bristling with weapons, overflowing with cash and potentially backed by the US Navy, (hey look, we're not at war for once. which means we're capable of an America-fuck-yea moment at any given time...) India has surpassed them in population, and is employing its own soft power projection in the region.

India is going to literally run diplomatic circles around them. Not that India is perfect by any stretch, but they're a vastly more palatable business partner than China. Unless you're a dictator.