The Soviets managed to invade Iran in the middle of Barbarossa, so an invasion of Iran should be even easier in August 1940. The Soviets would gain control of most of world's oil reserves, enabling them to black mail other powers and charging extortionate prices for oil. The Soviets would only need to devote a small portion of their armored force to accomplish the task of taking the Middle East given the poor state of British defenses. I believe the Soviets also had the largest airborne force. Taking a lightly defended strait of Hormuz shouldn't require a herculean effort on the part of Soviet airborne divisions.
And everyone's just... going to be fine with this? Like, I imagine the Nazis, who are already chomping at the bit to kill as many Slavs as they can are going to have a slight issue with not doing a damn thing as the Soviets gain that much control over a resource they were lacking. The Nazis aren't going to be happy being over a barrel like this. Aside from all the other issues with your points, this just makes the Nazis breath takingly stupid for allowing the Soviets, the nation that they're planning to conquer and slaughter is people, that much power over the world's oil supply. There's no logic to it.