How was the Chinese study of linguistics before the arrival and influence of European scholars?

So in that thread there was the point made that the start of modern linguistics in the West can be linked to the mid-1800s when people were beginning to look at how Sanskrit and Greek and Latin compared. I'd made the point that you could also argue that it began in 1968, and that anyway in China they'd already been doing their thing well before people like Jakob Grimm came around.

What I'd said that you'd asked for clarification on was this:

In China, while there were people who were influenced by the goings-on of people like Grimm & co., they'd already been doing their own sort of modern linguistics since at least the 6th century CE, and an earlier form in at least the 3rd century BCE.

What I was referring to here was, first, the roughly Tang period (6th-7th century or thereabouts) and the linguistic traditions of the time, and then about the 3rd century, the Han period. I'd add a third period of the late-Qing/early-Republican period, where a number of now-well-known scholars were, through opportunities like the Boxer Indemnity, getting Western educations and thus brining back those methodologies to China. So let's call those Early and Middle Dynastic, and Early Modern. I'll briefly outline the state of the field for each below.

#Early Dynastic

The beginnings of what we know of the study of linguistics and language in China had more to do with philosophy than what we're doing today. The proper use of language was an important part to multiple philosophical schools. When I say proper use I don't mean having good grammar. Rather it was the idea that a king should be the thing that "king" means. You should fit your label and strive to live up to it. This is a topic that people have spent millennia discussing so I'll cut it short here.

However several significant works that are more linguistics and less philosophical were also produced in the early dynastic period. The Erya 爾雅, Fangyan 方言, Shuowen 說文解字 and the Shiming 釋名 were all important language related texts published around that time. They cover various topics including etymology, pronunciation, usage and dialectal variation. These formed the foundation of the study of linguistics in China for millennia to come.

Also in use at the time was a system known as the fanqie 反切 pronunciation system which was a way to write down the pronunciation of a character using two other characters. So characters read da1 plus tong4 gets you dong4. This was a way to document pronunciation even though there wasn't an alphabet to do that in. The system has lasted thousands of years. The reason for this, and why it's so important, is even this early people recognised that language had changed considerably enough that earlier texts were already becoming difficult or impossible to read, so this was part of a larger sense that these needed to be preserved as meaningful texts.

#Middle Dyanstic

The Tang, around the beginning of the 7th century, is another major milestone. It was in this period that we start seeing more detailed accounts in a more systematic way of pronunciations. Things like the rime tables became an invaluable tool for language documentation and for keeping track of earlier pronunciations. In fact this same system is still used today, and you're not going to be able to access a lot of the modern literature on Sinitic phonology if you're not fairly familiar with the system. Even in the face of all the changes brought in the Early Modern and Modern periods, the early ways of organising and analysing the languages are still very much present.

It's also these rime tables, by the way, which represent to some extent the common ancestor of Mandarin, Cantonese, Hakka, Wu, Xiang and others in the Sinitic language family, so much of the data that was documented in the 7th century is absolutely invaluable today for understanding how the modern languages developed.

And of course we also have a good number of texts documenting changes in grammar and uses. One of the most important is the Nogeoldae 노걸대 / 老乞大, first published around the 14th century. It's a textbook on colloquial Chinese written for a Korean audience, and tells us a lot about both languages of the time. It's not the only such text, but it's one of the more well known ones.

#Early Modern

Of course there were changes around the start of the 20th century, as should be expected for a period of such monumental changes.

What is probably the most significant factor that led to a major shift in how linguistics was done in China began with the end of the Qing and the early Republican period, including things like the May Fourth movement and an effort to cast of foreign imperialism by adapting and adopting foreign practices. A huge part of this was the Boxer Indemnity Scholarship Program and its recipients like Y.R. Chao (趙元任) who I personally consider the farther of modern linguistics in China.

Chao was a phenomenally influential force in the study of linguistics in China and through his education at Cornell and Harvard brought back to China the modern philological methods and really jump started what was to become a significant tradition of dialectological documentation. His 1928 work Studies of Modern Wu (現代吳語的研究) as well as his grammar of spoken Chinese were both ahead of their time in the manner and detail in which they described and documented natural speech.

Of course you also had the political side of things, with the push for the vernacularisation of literature, and various attempts to make the standard more accessible as well as more useful in terms of modern vocabulary. Politics and philosophy have never been separable from linguistics in China, if they have anywhere in the world.

So I hope that helps explain some of the older traditions. Since there's not a specific question I've given just a more broad overview. But if you have follow up questions let me know and I can expand on any of the above.