@regularkid Wow, 5 pages after a week from the original post is impressive.
I think it can be said that Outer Mongolia was for the Soviets almost what Inner Manchuria (Manchukuo) was for the Japanese.
If the game doesn’t want to add scarcely worthwhile complexity, the most reasonable way to represent all of what we today know as Mongolia is simply as Russians but originally owned by none (or Chinese). However, the importance of the Mongolian military itself was negligible.
By the way, when (in violation of the non-aggression treaty) the USSR declared war on Japan, “Mongolia” was a base of operation for the invaders. So, the Russians didn’t need to have someone else declaring war on them, to turn their Mongolians into Russians. That already practically happened before the start of WW2, regarding the Russians ability to move freely within Mongolia.