"The Russians did not stock much ammunition for these guns..."
Huh? They stocked millions of rounds for their SMGs and the ammo was the same for the Tokarev pistol. Nor was the Tokarev ammo different enough from the German Mauser ammo to cause any problems. The Mauser was still in service in some Russian units through WWII, and they used the standard Tokarev ammo in them. If the myths about super power Tokarev ammo are true, the Russians wanted to blow up their own guns, sort of odd behavior in wartime.
The Germans also modified tens of thousands of captured Tokarevs to use the 9mm 08 cartridge, which it does with the original springs and magazine with no problem. If the 7.62mm pistol round is so powerful, guns made for it should malfunction with the "puny" 9mm. They don't.