But the concept of China, Zhong Guo, 中国 was in the minds of the people even in this periods as Warring states, 3kingdoms, 16 kingdom... and so on.
By chinese philosofy, the China will ever broken and re-united again... That means the comunist china will fall down some day, but the China will re-united again and again.
Why Henry I and II didn't was German kings also?
And these kings at these times have so many titles, I guess Barbarrosa was also king of Italy.... So that means he can be an alternative leader to Italy too.
I'm impressed: you can tell what was in the minds of people 2500 years ago. I can only sometimes tell what my wife is thinking today . . .
In fact, while the term Zhong Guo was in use as far back as the Zhou Dynasty, its meaning even in the fragmentary written sources keeps changing. It was not until the Song Dynasty (960 CE) that writers start using the term to mean the 'trans-dynastic' civilization with a common ancestry, language, and culture and a set territory (Reference: Tackett, Nicolas,
Origins of the Chinese Nation. Cambridge: Cambridge University Press, 2017, pages 4 - 280). Before that, it could mean anything from the capital city to the region around the capital to a limited geographical area of the Chinese feuding states - and sometimes, as in Han Dynasty records, it could be used with all three meanings depending on context.
What the people thought of this is unknown and unknowable, but in popular writing (primarily poetry) which might be a possible indicator, more often the dynastic names: Han, Tang, Great Qing, etc are used instead of any 'generic' term for 'China'.
In that, then, China is Identical to Germany. Neither peoples had any concept of political loyalty to any generic Chinese/German civilization until very recently (Zhong Quo is first used as an official term in a Chinese government document in 1689 CE in the Treaty of Nerchinsk by the Qing to mean China as governed by the Qing, which makes it actually Later than the concept of an official Kingdom of Germany, which appears in the historical record 800 years earlier). Both were identified and self-identified themselves according to their cultural and linguistic similarities - the Chinese as far back as the Warring States and the Germans at least as far back as 200 BCE, when Roman writers begin identfying a distinct and recognizable group of tribes with similar languages, customs and appearance as "Teutons" or Germans - but no political unity at all.