Might the West have overestimated their capacity: probably yes (especially in later years), but the conflict was still very real.

Yes, that was the Soviet (Russian) perspective. They felt pressured to keep up with the US. But the flipside is that the inverse was also happening; America spent tons of money developing new weapons and capabilities because the Russians were doing the same. For instance, the F-15 was developed into the air superiority fighter that it is because the Mig-25 was (mistakenly) believed to be similarly capable.

Too often the "Soviets were afraid of America" narrative is used to suggest that America was an aggressor and the Soviets were hapless victims of this aggression, forced to spend by America. But the truth is that both sides were doing this to each other, and besides, the whole of it was arguably started by aggressive Soviet expansion before and after WW2, for instance the Molotov–Ribbentrop Pact in which the Soviet Union conspired with the Nazis to divide up Poland, Russia's subsequent refusal to allow Poland to become independent after the war, and the persistent Soviet threats to invade western Europe and incorporate France, the UK, etc into their "union". The "Soviet Union" was a farce of a union, a fig leaf over Russian imperialism.