Why didn't the USSR invade Mongolia or China like they did in Eastern Europe and the Stans?

I'm only tangentially into research on this topic, but as far as I know the leading researcher on Soviet-Mongolian relations is Sergey Radchenko, who published the book 'Unwanted Visionaries' on the topic as well as at least one other paper, which I'll look up if there is any interest in the topic.

For a simplistic answer, between 1911 and 1946 the legal status of Outer Mongolia was disputed, as it was still technically part of Imperial China, though completely autonomous. Mongolia had a puppet regime installed early on in the life-span of the Soviet Union (1921). The UN finally recognised Mongolia as an independent State in 1946. After ceding military basing rights and economic concessions to the USSR from the 1920s onwards, Mongolia was largely unimportant in Soviet foreign policy, so there was a Soviet armed presence in Mongolia, but not in an interventionist sense.

As for China, the complex geopolitics after the Second World War meant that whilst the Red Army occupied Manchuria after the war, strong US Democratic Party support of the Nationalist (KMT) Chinese, and Stalin's desire to remain on good terms with the Western Allies in the immediate aftermath of the war, meant that open support by the USSR of the Chinese Communist Party (CCP) was not possible, though they also took little overt actions to support the KMT in their areas. The Soviet-Western relationship increasingly broke down in 1946-7, coinciding with the withdrawal of the Red Army from Manchuria, and to show tacit support for the CCP, much war-making materiel was left behind or passed directly into the hands of the CCP, greatly boosting its capability to fight the Chinese Civil War. From 1949 after the CCP's victory in the Civil War through until the Sino-Soviet Split beginning in 1956, Mao acted as the junior partner to the USSR's brand of communism.

Thus to answer the original question, the USSR did in fact invade both Mongolia and China, however the methods were much less direct than those employed in the occupation and Stalinization of Eastern Europe between 1945-1956.