After the Manchus forced a territorial settlement on Russia with the battle of Albazin and treaty of Nerchinsk, and then the two states followed this us with the Treaty of Kiakhta in the 1740s, both sides generally saw themselves as "having a good thing going" and tended to have a remarkably peaceful relationship, with no other territorial expansion at the others expense until 1858-1860 (Russian gains were also made with more diplomatic finesse and less Chinese bitterness than the contemporary opening of treaty ports), and no big bilateral crisis until the Ili crisis of the 1870s.
There were good reasons for this - both powers were overwhelmingly focused on things other than a mutual rivalry, and in these circumstances, diplomatic accomodation proved workable.
...But tensions did exist, war was possible at times, and it is interesting to speculate how the Russians and Chinese would have stacked up against one another during the reign of Qianlong (1735-1799)
---I see two main scenarios for this, an earlier one based on Manchu aggression, and a later one based on Russian aggression. I welcome tweaks for making a conflict more realistic, and thoughts on the sides' relative military capabilities and performance, and their possible diplomatic and strategic objectives against one another.
Scenario A) Qianlong determines on a campaign to reduce Russian power and chastise the Russians, in the tensions brought on by China's demands for the return of the body of Dzhungar chieftain Amursana (the campaign against Amursana was what in OTL resulted in the Qing Dynasty's conquest of Xinjiang and Tibet), and Russia's refusal to return the body.
Tensions were fairly high starting from 1758 for the next few years. In OTL, the Qing threatened to cut off trade and besieged the Russian Orthodox monks authorized to reside in Beijing.
The Qing had finished several victorious campaigns and extended their territories and crushed vestigial Mongol resistance. They had built up a skill set for war on the steppes that allowed them to win.
If they are sufficiently angry at the Russians they should be able to mount an offensive gravely threatening Russian territories in eastern and southern Siberia.
Qing territorial objectives, if Qianlong gets greedy, could include seizure of the Buriat Mongols' lands, the silver-mining ditrict around Nerchinsk, and a band of the fur-rich forest country north of Manchuria.
At this time, the Russians are busy with the 7 Years War. Qianlong could conduct his war on an entirely independent basis, but the British could conceivably take an interest in the campaign.
Fighting the Russians would probably at least reveal they were stronger than in the 1680s. It may or may not be sufficiently disturbing for the Chinese to become interesting in cooperating with the British in terms of purchasing certain types of arms and renting naval assistance. Frederick in Prussia would be incapable of reacting to the situation except simply to pray that Chinese attacks divert Russian forces from Europe. The seed would be planted over the long run in Prussian thinking of the potential of China as an ally. If a true coalition war develops, Qianlong long may try, and succeed, in having French missionaries and traders ousted from Vietnam. In the long run, this might divert French colonial interests offshore to Okinawa and Taiwan in the nineteenth century.
Scenario B) - Catherine the great gets the wild idea of recovering territory (and glory) on the Amur, and gambles to establish a trading empire along the lines of the emerging British Raj in northeastern Asia. The occassion or provocation she can seize upon was the the Qing's solicitation of Catherine's vassals, the Torghut Mongols, to migrate from the Volga back to Mongolia/Dzungaria in 1771.
Russian Chinese cooperation was built in OTL on a degree of expectation that the two sides would return each other's fugitives, but the Qing dynasty as part of its strategy of in-gathering the Mongols essentially stole potential taxpayers and soldiers from Catherine, so this could be used as justification for a conflict in the 1770s if Russia chooses on.
The near-term territorial objectives would be focused on seizing the Amur and more of the Pacific coast to support Russian trade in the Far East and North America. From 1774 onward, there is a break in the wars with the Turks, and Suvorov could be available for service against the Manchu banner armies. How would he do militarily?
At this point in time, 1775 and the years after, Russia has a fairly peaceful environment in the west, and China has no one in Europe likely interested in becoming a coalition partner, as the Atlantic powers are abosrboed in the American revolutionary and colonial wars. Actually, the Turks and Persians might be most interested in allying, but they may or may not be capable of getting involved at this point.
Thoughts on A or B or other takes on the same overall theme of the post?