Once upon a time, the USSR had 'useful idiots' as apologists in other countries.
Putinism ("nothing is true and everything is possible") has developed well beyond that - the encouragement of 'useless idiots' in other countries is proving much more effective.
We'll ignore the various tussles of the British and French over colonies - the smaller countries got what the French and British weren't so bothered about.
From the point of view of the Imperialists, India was the Empire, it outweighed everywhere else in significance and was also key to the...
There's an argument that the history of Russia is a case of acquiring territory as part of the process of protecting territory that it's just acquired - something not uncommon with imperialist/colonialist countries, of course, but likely to bump into the interests of other powerful countries...
The Chinese will do whatever appears to them to be in their best interests which is unlikely to include harming their major markets. I'd suggest that a pariah Russia, largely dependent on Chinese goodwill to survive, would look like a wonderful colony of exploitation.