Earlier quoted context omitted.
The Soviet Union was able to innovate in the areas they chose to sink resources into but innovation was clearly not as widespread as evidenced by their decades of stagnation from the 60s onwards. They were still innovating in military technology in the 80s but analysis since their collapse analysis that they were at least 20% of GDP on defence, if not as high as 40%. The West managed to match and surpass Soviet milit…
I'm not trying to downplay their accomplishments, but how much of their scientific advances from the 40s-60s were due to capturing ex-Nazi tech (and scientists) or stealing from the US via their incredible intelligence efforts?
They definitely supported a lot of their rocket science from found documentation in Peenemünde et. al. (The personnel OTOH did its best not to fall into Soviet hands, and most of them ended in America, even though some didn't make it and were captured by the Soviets.)
They had genuine excellency in mathematics and theoretical physics. First, those specializations didn't require much expensive or advanced equipment back then. Second, by their very nature, they were freer from ideological bullshit than other specializations, and that alone attracted many of the best and brightest there.
(I can confirm that even in late-stage Communist Czechoslovakia, very hard sciences were considered an intellectual haven for non-conformists. The ideologues didn't understand them and did not consider them subversive per se.)
On the other hand, biology was under full tyranny of Lysenko et. al. and "bourgeoise geneticists" would get imprisoned in concentration camps and even executed or starved to death. As a result, Soviet biology never recovered to a respectable science again, not even after Lysenko lost his power.
Until today, you will find ex-Soviet textbooks of maths and physics all over the net, and people actually download them and use them to study. That does not apply in most other domains.