You are basically arguing about "egg and chicken". How do you expect someone to become Chinese culturally or legally without being welcomed into the fold in the first place?
If you read Chinese you should have known that in the concept of 诸侯用夷礼则夷之,进于中国则中国之, the last sentence means that "a foreigner who embraces Chinese rite/礼 should be treated as Chinese". The concept is about whether one sincerely want to become instead of already being.
Once again, history is your best teacher. At the begining of Zhou dynasty, Wu, Yue and Chu states were regarded as non Chinese by the states in central plain. But once they paid homage to the King of Zhou they are part of China and respected as such. Taking an oath to act like Chinese is enough. BTW, that oath is nothing as light as the oath taken to acquire US passport.
It is hard for foreigners like you to understand the meaning of being Chinese, but also easy for "foreigners" like Eileen Gu once they went through the journey to become Chinese. Becoming Chinese is like believing in God, one does not need to be able to cite the bilble, pray, be familiar with the rutines, one just need to take a deep breath and commit.
For someone who seems to like to "gate keep" who is Chinese and who is not, you don't seem to know your Chinese history very well.
Just to take the example of Chu. Archeology has already shown that the early Chu state was nearly identical to the Zhou in culture (indicating they were an off shoot of the Zhou, or an out right Zhou colony), but "barbarized" over time as they conquered more territories of peoples who were not Zhou. This insight is reinforced by the fact that the earlier you go in Chinese history records, the
more Chu is regarded as Chinese - a careful reading of
Zuo Zhuan indicates that Chu was
never associated with the Manyi (ie "barbarians") in
Zuo Zhuan, but that later, Warring States period texts
did treat Chu as barbarian because its kings began to claim themselves as barbarians in order to reject Zhou rule and assert their own independence.
In other words, it's not that Chu started off as barbarian state, but became accepted by the other Zhou states once they swore fealty to the Zhou and adopted Zhou rites. But that they
chose to
reject their originally Zhou/Huaxia lineage, both in order to better rule their "barbarian" subjects
, and because they wanted to make out right play for cultural and political independence from the Zhou kings as the latter's authority faded during the Eastern Zhou.
It was only towards the end of the Warring States that, again for political convenience, Chu re-asserted its "Huaxia" identity because - surprise surprise - it became an asset as Chu sought to assert hegemony over the Central Plains states as its territories encroached upon their borders. Even so, many in the Central Plains states distrusted Chu - there was never this universal belief, as you seem to assert, that Chu became Chinese as soon as they paid homage to the Zhou kings.
Or as Yuri Pines put it in his highly cited 2018 re-analysis of Chu identity:
"The new understanding, summarized by Xu Shaohua in the seminal volume by Constance A. Cook and John S. Major is that “there is little archeological evidence of a distinctive Chu culture during the Western Zhou times.” It was only from the Springs-and-Autumns period on that a divergent cultural pattern associated with Chu began emerging, and even then Chu’s elite culture remained strongly conformant with the Zhou ritual practices. This suggests an entirely different cultural trajectory: Chu was not a “barbarian entity” attracted by the glory of the Zhou culture as hinted in the Mengzi, but a normative Zhou polity that developed cultural assertiveness in tandem with the increase in its political power."
Such a basic lack of nuance on the understanding of Chinese history indicates you're really talking more in stereotypes and generalizations than deep recognition of what went on. There's no shortage of historical states and dynasties that manipulated the optics of identity for political gain - leaning towards "barbarian" when it was beneficial to do so; and leaning towards "Chinese" when it was beneficial to do so.