Didn't Putin say, or at least infer, that he wanted to recreate the borders of the former Soviet Union?
No.
I saw an article from 2014 that cited John Bolton saying that Putin saw the collapse of the Soviet Union as a major geopolitical disaster of the 20th century for the Russian nation because tens of millions of Russian speaking "co-citizens" and "co-patriots" found themselves in the former Soviet Socialist republics outside of Russia. Bolton commented that Putin wanted to bring all of those "co-citizens" and "co-patriots" back under the umbrella of a new Russian empire. To bring those former Soviet citizens back, the land that they lived on had to come along too.