Today 92% of the population mainland China are of the Han ethnicity. 150 years ago, did the majority of the population see themselves as Han, or one ethnic group under Qing rule?

Something to note is that "Han Chinese" doesn't really necessarily refer to any specific ethnic group; a Han Chinese would be someone who was Sinicized and followed common "Chinese" belief systems and values. We can see examples of that through the repeated Sinicization and assimilation of Turkish and Central Asian tribes into the mainstream Han empire.

By the late 19th-century, the Manchu Qing had already adopted most of the traditions of the Han Chinese, becoming Sinicized after centuries of being immersed amongst the overwhelmingly Han majorities. Although, newer schools of thought are suggesting that the Qing retained a higher level of Manchu culture than previous historians had suggested.

Check out Zhao Gang's 2006 paper in Modern China vol. 32, no. 1: "Reinventing China: Imperial Qing Ideology and the Rise of Modern Chinese National Identity in the Early Twentieth Century". I have the PDF if you're interested and don't have JSTOR access. Also, keep in mind that this is a pretty politicized and highly debated area of Chinese history.

A choice excerpt is:

...First of all, rulers of China, whether indigenous or foreign, had often redefined the scope of China to suit their needs: the Manchu rulers were not concerned that equat ing Qing with China would lead to the loss of their Manchu identity. Second, if they publicly embraced the concept of China, such acceptance of Han cul ture would win them the support of the Han people. Given the political bene fits, it is not surprising that the Qing rulers quickly adopted the term as a stan dard synonym for the Qing state in foreign affairs. The Qing court's routine use of China to refer to its state in treaties, diplomatic correspondence, and so forth most clearly demonstrates its identification of China with Qing. De spite shifting political conditions, the Qing rulers from Shunzhi to Qianlong always held to the equation of Qing with China, only adjusting the latter's scope to match the expanding Qing territory. (Zhang 2006 pp. 7)

This essentially goes to show that while later Qing became increasingly Sinicized (the ethnic Manchu garrison in Beijing intermarried with local Han and eventually became unable to speak the ethnic Manchu language entirely), they originally saw the "Han state" as only a single portion of their multiethnic state, only choosing to adopt Han customs because it was politically convenient. And as the last sentence mentions, the umbrella of what constituted "China" was continually expanded as the Qing territory expanded.

Zhao mentions another example:

The conflation of Qing and China was taken up by Manchu officials serv ing in the court. In the 1720s, a Manchu official named Tulisen served as an ambassador to Russia ... the Manchu and Chinese versions of his book use China - Dulimbai gurun and Zhongguo many times to refer to the Qing state; only once does he employ the phrase Daicin gurun, Manchu for "Great Qing state."

This also goes to show that the Qing, although somewhat seeing themselves ethnically distant from the Han, were utilizing the very Han concept of Zhongguo as a political term.

By the time we reach the highly nationalistic period of the very early 20th century, just after the specific period you mentioned, the idea of a cohesive "Chinese" composed of the many ethnicities has emerged. Kang Youwei, prominent late Qing scholar, wrote (as quoted in Tao Xu, 1995: pp. 201):

"[The Qing government] should establish as [China's] permanent national name the Chi nese state (Zhonghua guo). Because the Manchus, Han-Chinese, Mongols, Muslims, and Tibetans all belong to a single state, they are all Chinese (Zhongghuo ren) without any distinction".

So, as a final wrap up, the Han were seen as a single ethnic group under the umbrella of the Qing Dynasty; however, the other ethnicities (including the Manchu Qing) adopted many aspects of Han culture for political and sociocultural reasons. The idea of unified "Chinese identity" is elegantly represented by the five stripes of the first flag of the Republic of China: Han (red), Manchu (yellow), Mongols (blue), Hui (white), Tibetans (black).

Sources

Zhao, G. (2006). Reinventing China: Imperial Qing Ideology and the Rise of Modern Chinese National Identity in the Early Twentieth Century. Modern China, 32(1), 3-30.

TAO XU (1995) Wan Qing minzu zhuyi sichao (On the nationalist trend in the late Qing). Beijing. Renmin chubanshe.

EDIT: If you are interested in some of the drama that's going on in China about this theory of Qing ethnicities, read this article:. I'm from Singapore and studied in the US, so I'm relatively skeptical of the somewhat blatantly politicized attacks of "New Qing History", but, hey, check out both sides and decide for yourself.