I can speak in regards to Iran. Stalin did have ambitions to expand at the very least indirectly influence into the country. But first, let's take a step back.

One thing to keep in mind is that the Russian Empire, and later the Soviet Union, has had both direct and indirect control of Iran via spheres of influence, annexing territory, funding communist groups after 1917 (and especially during Stalin's reign), etc. So Stalin's ambition to exert influence on Iran isn't the most shocking thing to hear. Non-historians in Western nations mostly think of US and British influence in Iran due to the 1979 Revolution and subsequent events, but Russian/Soviet influence is a major aspect of Iranian history that has had a major impact on Iran that still has lingering effects to this day (it's also ignored in the current regime's rhetoric due to their ironic alliance with Russia, but I digress).

Maybe I'll expand more later, but I'll give you one example that highlights such ambitions. When the Soviets and British invaded Iran in August 1941 when Shah Reza Pahlavi refused to renounce his support for Nazi Germany, the Soviets and British jointly occupied Iran. The son of Reza Pahlavi, Mohammed Reza Pahlavi, was made Shah and the British occupied the southern half of Iran whereas the Soviets occupied the northern half with the stated intention of an eventful withdrawal. Iran ended up being a crucial part of supplying the Soviets via the Lend-Lease program and the Allies in general with oil production.

The Nazis were defeated in May 1945, and the British and Soviets agree to mutually withdraw their respective military forces in the country within six months of the end of all major hostilities (the British were still at war with Japan and the Soviets were preparing their invasion of Manchuria).

In September 1945 however, the Azerbaijani Democratic Party, with Soviet support, was formed. Via Soviet arms, training, and direct intervention by the Soviets preventing Iranian state officials from intervening, by November 1945 the ADP controlled all of Iranian Azerbaijan, and declared the "Azerbaijani People's Government". Meanwhile, in Iranian Kurdistan, in December 1945, also with help from the Soviets via the same measures above, Kurdish forces formed the "Republic of Mahabad". (All I'll say...is that with the 20 year rule we can hopefully talk about certain...more recent events starting in 2034 and especially 2042)

In response to this, the US exerted intense pressure on the Soviet Union to force their withdrawal from Iran. In January 1946, the US pushed for the UN Security Council to vote on the issue via Resolutions 2, 3 (in April 1946), and 5 (in May 1946).

The US threatened to use force if the Soviets did not withdraw from northern Iran, and by March 25th, 1946, the Soviets withdrew from Iran, but the crisis lasted until mid-December 1946 when Iranian troops were able to move into the Azerbaijani and Kurdish regions and regain control of the territories.

The Iran Crisis of 1946 is just one example of Soviet influence in the country. Perhaps I'll expand on this post if requested.

Some sources:

Russia and the West in Iran - George Lenczowski

The Cold War International History Project (this one is super cool to check out since there are declassified documents and such)

"The Iranian Crisis of 1945–1946 and the Spiral Model of International Conflict" - Fred H. Lawson - International Journal of Middle East Studies, Vol. 21, No. 3. (August 1989)

Edit: I added some sources in case people want to dig deeper.