This misses a pretty key point that the western powers embargoed Japan right before the Nazis invaded the USSR. The “move North” strategy stopped being practical when they didn’t have a way to get oil for that invasion.
Significant Soviet forces stayed there until 1946 - and they've tried to annex parts of Persia/Iran.
Though in 1942-43 when Soviets had to expend an enormous effort and spared no resource to annex back places like Stalingrad, the Soviet forces in Persia still stayed put. Their mission was seen utterly important.
The North African campaign was similar in that it was partly an attempt to get to the Arabian oilfields, but fought over the top of at the time undiscovered Libyan ones.
They actually almost got one of the cities but Fall Blau was a total desaster and the German spearheads were opposed by to many soviet troups.
The oil back then came from the US, Soviet Union (Baku) and Persia.