Blitzkrieg was early combined-arms warfare; its modern iteration underwrites American military supremacy.
Zerg rushing is an r-production analog that uses swarms of cheap, expendable units to overwhelm the enemy numerically. This is closer to the Soviet (and now Russian) doctrine of using humans to absorb ammunition. It fails against combined-arms armies because it lacks manoeuvre. It works when the enemy is production constrained, e.g. Ukraine.
Zerg rushing works in video games.
The Soviets in WWII used human waves against the Nazis. That said, the USSR was capable of combined-armed warfare.
Russia has proved incapable of combined-arms warfare. They launched human waves in Bakhmut, and are largely using numerical advantages in raw recruits to push for marginal gains. This isn’t how a modern army fights.
The Red Army definitely used them against Finland. But you are right, they weren’t used against the Nazis.