https://en.wikipedia.org/wiki/Archduke_Franz_Ferdinand_of_Au...
People have been saying that for 69 years. I'm not saying it's a disturbing possibility, or that people shouldn't be preparing for it. But it's not as likely as you seem to think.
There's no comparison to the Crimea situation. Crimea was overwhelmingly pro-Russian, and had a strong independence streak (see: the sovereignty referendum of 1994). An amphibious invasion against a largely hostile population is an entirely different matter, and would not be pretty, even for a large power like China. There's also the small matter of the US navy and Air Force.
I also don't think the US (or Japan) are keen on moving the focus of Chinas expansion from Taiwan to the Senkakus, which is what would happen next.
There's a lot of factors at play, it's a larger issue than just comparing two mismatched militaries.
It may provide a distraction for further Russian expansion, but Russia clearly doesn't need any new foreign precedent to justify invading it's neighbors.
> If China then decides Mongolia too is part of greater China, who can really stop that? Nobody.
China taking Taiwan might not start a major power war (though given the history of such wars, I wouldn't dismiss it as easily as you do), but Mongolia is much more likely to (with Russia as the opposing major power.)
Russia gets expansion in Europe. China gets expansion in Asia. They agree to try to stay out of each others way. It certainly wouldn't be unusual, historically speaking, for very powerful authoritarian regimes to reach agreement on annexations of territory.
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.
There's no scenario where China doesn't get Taiwan, unfortunately for the people there. The only question is what that's going to look like. The rest of the world will do nothing about it, other than wave their hands around frantically. When it happens (during Xi's lifetime), it's going to set a particularly terrible precedent that will encourage Russia to do more of the same in eastern Europe. If China then decides Mongolia too is part of greater China, who can really stop that? Nobody.