Even in the times of the Great Empires, there were always other great powers - perhaps not peers, but powerful enough to be truly independent. This era most of us grew up in where the US was this unchallenged global hegemonic power was a major outlier in history, owing exclusively to rare circumstance. That being that after the USSR suddenly collapsed, there were not only politicians in the US that wanted to be rulers of the world, but also no other powers that could even remotely compare on a technological or economic level except Japan. But Japan itself also began a rapid economic collapse just about the time that the USSR collapsed.

And now not only were these circumstances rare, but they were also inherently liminal. Technological and economic edges fade rapidly, especially in light of major population level differences. I see no reason to think China imagines they could or even wants to be anything like the US was 30 years ago. The world is returning to its more natural multipolar state, as it's more or less always been.