This is an excellent question and Im super happy you asked it. Because this is actually more or less what I research; this question basically asking what Chinese national identity looked like in the warlord/early Republican period. Im going to break this answer down into two different parts; a brief introduction into how the Han (the ethnic group making up ~95% of China, what we call "Chinese" in English) expanded in years past, and then how the borders of China were shaped and justified in the Republican period.

Pre-20th Century Expansion

Note that this section will be brief, and not as in-depth as the latter. I am no expert before 1900 China, and I'll leave that to more qualified experts.

The Shang Dynasty is currently accepted by most historians as being the first "developed" complex civilization of Han Chinese in China. This dynasty developed around the Yellow River valley area, so we're talking about north-centralish China, modern day Shendong and Hebei, Henan, etc. Its important to understand that at this period of time and far beyond China is way more culturally diverse than it is now a days. These Han societies were trading and diffusing ideas with, as well as conquering, neighboring cultural groups that would eventually become assimilated or decimated. Mark Edward Lewis's book Sanctioned Violence in Early China covers a lot of this development until the Han Dynasty. Keep in mind that while the Han Dynasty is considered by some to be the first "unified" Chinese state, its authority is quite weak over the southern part of China and its influence barely extends West. Lhasa, Tibet was still quite some ways from Chinese civilization. Heres a map: https://www.britannica.com/topic/Han-dynasty#/media/1/253872/236466

Chinese conquest becomes quite stagnant after the Han, with some more conquest in the West by dynasties such as the Tang and Sui, but this is generally focused around the Silk Road trade routes. Life in what is now Western China was rough in those days, not only is it mountainous and has one of the world's most inhospitable deserts, but it was also mainly inhabited by a plethora of what the Chinese called "barbarians," who were interested in their own share of that wealth along the Silk Road. Here's a map of the Tang: https://www.chinahighlights.com/map/ancient-china-map/tang-dynasty-map.htm . As you can see, there really isn't much addition inside modern China, but do note the loss of Korea and Vietnam.

This stagnant growth of territory is broken when the Qing Dynasty arrives in the 17th century. The two major conquest-minded emperors of the Qing are Kangxi (1661-1722) and Qianlong (1735-1796) emperors. Here's a map of Ming China: https://www.chinahighlights.com/map/ancient-china-map/ming-dynasty-map.htm . Here's a map of the Qing at its height in the early 19th century: https://www.chinahighlights.com/map/ancient-china-map/qing-dynasty-map.htm . As you can see, the Qing form what we know as the territories of modern China plus more, bringing China to its territorial zenith.

But these are all just maps of military and cultural expansions, and what makes them irrelevant to the question is that the concept of nationalism and identity didn't really exist like it did in the West until the 20th century. For the Chinese, these lands were subjugated because they were inhabited by inferior people. There was no concept of Westphalian diplomacy and sovereignty (much to the Europeans dismay when they attempted to open relations with East Asian societies) and nationalism didn't exist. Chinese expansion was forced into a halt by the late 18th century (in 1792 the Qing failed to conquer Nepal). Faced with huge domestic problems this expansion brought there were various rebellions starting with the White Lotus Rebellion in 1794 that began a steady decline of Qing power in Asia which was exacerbated by the arrival of Europeans who would arrive just in time to quite literally beat the shit out of the Qing. These foreign conquests albeit small (Hong Kong and Macau) would have a pretty long lasting affect of the mentality of future Chinese nationalists who would coin the term "Century of Humiliation" to refer to the 19th-mid-20th century.

Identity and Sovereignty in Early Modern China

In 1911, the Qing Dynasty falls apart and Yuan Shikai becomes president (i.e., dictator) of China. But the position is much more a title than a reality; China splinters into several different states. In 1926 the Northern Expedition sees the Kuomintang unify much of Eastern China, but still failing to take the Northeast (or Manchuria), Mongolia, and the Western parts of the the former Qing Dynasty. China is in huge disarray, and there's one thing causing it: Confucianism! Just kidding.

A new class of people mainly being educated in Britain, America and especially Japan, are fed up with China being bullied by foreigners and fraught with domestic troubles. While they do blame Confucianism for most of their problems (labeling it 'feudal'), they understand that China needs unity to prove it is strong. Why do they understand this? Because Western-based nationalism dictates that for every strong empire there is understood to be a sort of "core" area; the motherland where a single cultural group dominates society. It is imperative that this "core" area be of one state. This is extremely psychologically important for nationalists:

The purpose of any (national) identity is to regularize behavior so that uncertainties can be minimized and life rendered more manageable. The function of a national identity is to sustain the state by unifying the population, at least psychologically. The state is important because it has historically proved to be the most effective unit of human organization to provide for the physical survival of a sizable population. Moreover, national symbols with which people identify arouse feelings, fulfilling primordial, affective needs. An emotional identity with the state as an embodiment of the combination of many common elements of the population also reinforces national distinctiveness, which justifies the perpetuation of the state. - Dittmer & Kim, 32.

Woah. This is pretty different from the traditional ideas of "my race superior, yours is not!" There's a lot more nuance and more importantly, justification. Political justification as to why China should be... China. But that leaves the question, what is China? Is China the Ming borders, a dynasty which was ethnically Han, or is it the Qing borders, a dynasty that was not ethnically Han, but Manchu? Does China have a right to exist in the modern world?