[adventured]

It might be a question of whether it matters, given the vast territory they already share (which if I'm not mistaken is already nearly the length of the Russia-Mongolia border).

Granted, for a long time now Russia has harbored paranoia about their vast empty East, and that China might one day want to push into it. Russia is depopulating and China is overflowing with people. The comedy of the situation, is Russia having used the ethnic Russian setup premise to seize territory in Ukraine - China could use the same argument in various territories in Eastern Russia.

That said, I don't see Russia being willing to fight over Mongolia. China is already far too powerful and economically capable for them to do that. Russia could never come close to managing to hold off China in Mongolia, I think they know that. And I don't think Russia would be willing to go nuclear over Mongolia, which is what it would take to stop China if they wanted to annex the country.