The standard narrative I hear is that with the Manchu conquest of China, "captive Chin conquered her conqueror" and the Qing emperors were thoroughly assimilated into Chinese culture. But there are a lot of details that don't seem to match this: the imposition of the queue is an obvious one, as well as the continued importance of Manchu ethnicity and smaller matters such as the imperial estates and hunting grounds in Manchuria. So was it a matter of code switching, speaking Chinese to the Chinese and Manchu to the Manchu?
This is a doozy. I suspect you already know most of what I'm going to say but at least for the benefit of others:
I don't think it's possible to say anything like 'on a scale from The Pope to Yue Fei, the Qing dynasty is a solid Kubilai and a half' or whatever, these things all get kind of murky. The Tang dynasty for example is considered canonically Han, but the founding family was from a frontier region with many non-traditional practices and had a few non-Han ancestors up the family tree. The pre-Manchu Jurchens too are an interesting lot as some of the Jurchen population around modern day Shenyang were already highly sinicized, living sedentary lives, before the conquest began as they were quite closely integrated with the Han population of Liaoning province. I don't think I can do any better than to point out some illustrative facts and let the reader decide for themselves.
So yes there are definitely many examples of the Manchu regime preserving its distinctiveness even very late into its rule. You already mentioned the mandatory queues (which was almost revoked at the beginning, and then went completely unenforced as the late Qing New Army units were formed). There's the use of Manchu script which lasted into the 19th century and was a preferred script for many of the Jesuits at court. There's the fact that some Manchus resisted practices like footbinding (which some Han subgroups also did). There's the colonial pseudo-ministry of the Lifan Yuan which was staffed by non-Han officials and deliberately sought to integrate frontier populations by demonstrating the frontier bonafides of the Manchu regime. In the constitutional reforms of the 1900's one of the sticking points was that the council formed to oversee it was staffed by Manchu officials exclusively. Many institutions had ethnic quota systems. There were exclusively Manchu units under the banner system (which coexisted with Han banners, the Han Green Standards, and local Han militia). The six traditional bu ministries were to be staffed by both Han and Manchu presidents. There were prohibitions on Han migration into Manchuria, prohibitions that totally broke down during the late Qing period.
From the Chinese side, a significant number of Ming officials certainly resisted Manchu rule, with racial / ethnic as well as cultural overtones to their rationale. Resistance could be in the form of suicide or simple refusal to take examinations or refusal to assume office or full on armed rebellion. Most significantly, I believe the Three Feudatories Revolt had a fairly realistic chance of ejecting the Manchus entirely. During the very late dynasty, some nationalists like Sun Zhongshan were quite critical of the Manchu regime and denounced them as foreigners. (But not all, Kang Youwei notably advocated for preservation and reform of the Qing as ruling dynasty.) So it is pretty clear that some sense of Manchu distinctiveness lasted until the end of the dynasty.
On the other hand the dynasty went to great lengths to prove their Chinese bona fides and their system preserved the social structure for the most part and very effectively co-opted the vast majority of elites. And since the Qing state apparatus was incredibly light relative to the vast size of China, the average Chinese commoner had little direct contact with the Qing government itself. Day to day life was mostly mediated by local gentry-scholar elites who simply belonged to degree holding families without holding formal office themselves. The most important social institution in late imperial China is of course the examination system, and Qing emperors went to great lengths to solicit exam takers, including affirmative actions to favor underdeveloped and/or unruly provinces and prefectures. The content of the exams remained classics of philosophy and literature and the body of critiques surrounding them with a small amount of consideration of practical administrative subjects. The Qing restored the postgraduate Hanlin academy, even though it was traditionally a center of Confucian dissent during the Ming. Both Kangxi and Qianlong furthermore embarked on monumental compilations (the Kangxi Encyclopedia, and the Four Treasuries of Qianlong) of Chinese knowledge and literary culture. This was certainly a deliberate demonstration of legitimacy in the traditional Chinese sense.
This is really scratching the surface, I've never read a book that specifically tries to answer this question one way or another, but I'm willing to bet somebody somewhere wrote a tome on it, perhaps in Chinese. I've gotten a general sense of the issue by reading a bunch of other things:
A general overview of late Ming to modern China is the Spence book The Search for Modern China.
A good overview of the Qing specifically is Rowe's China's Last Empire.
Spence also has a biography of Kangxi, and Mark Elliott has a biography of Qianlong, and Spence again has a microhistory set during Yongzheng's reign called Treason by the Book. These three emperors of course are the defining emperors of the dynasty and built the institutions that carried China into the open era.
Also by Rowe is a nice piece of microhistory in Saving the World which is a look into the upper elite bureaucratic class at the high point of Qing power.
If you're up to it you might make a go at Hong Lou Meng as it is a fairly authentic fictional, probably semi-autobiographical portrayal of elite Han life during the dynasty.
You're probably familiar with Elvin's work on Chinese socioeconomics but I think it's a little outdated at this point. There's a more up to date booklet on the late Qing through Republican periods specifically called Economic Change in China 1800-1950 by Richardson.