I don’t think they want to oversee another 3rd world province. Might as well leave the locals in charge and just extract their resources at a deep discount

Less likely than Mongolia.

China barely cares about its own far north, let alone Siberia. It would much prefer to have Russia as a client state ready to supply oil and gas in the case of a war where sea routes for those are cut off.

I'm not suggesting formal conquest of territories.

If Russia falls apart, and as the last grand colonial empire, it bloody well should, China should have a lot of influence over the regional pieces.

It's hard to imagine something this ingrained ending, but nothing is forever.