That way was the realisation (continuation?) of the “Great Russia” project. People may not have civil liberties, may be poor and terrorised, but the outside is terrified too.
Did the Ukrainians, Georgians and Estonians want nuclear standoffs with the US for its own sake? Did they want to invade Czechoslovakia in 1968?
Also, we're bad at geography, and "former soviet state" is easy / lazy.
Finally, I know lots of Ukrainians that grew up in Russia and vice versa, and can't really keep all the permutations straight. (As I can't for my colleagues from any continent.)
But I get your point, and now it makes more sense to me.
I see in Putin more of that monarchist strain — chauvinism from the times of Imperial Russia, which indeed was so much focused on that "RRR-Russian" identity, much more "blood and soil" ideology. And add to that Late Soviet state "efficiency".
Only for Westerners Soviet == Russian, which puzzles me absolutely.