In no world resembling ours are the Russians getting past the
Continental Divide in any sizable numbers. The Sioux aren't even the first tribe you meet on the other side, and the Russians would in fact have a good reason to aid this tribe (IIRC it would be the Shoshone or Blackfoot) against the Sioux.
I mean, the easy answer is nerf the US and Mexico because A) that slows Canadian colonization of its west and B) generally speaking IIRC the best bet for the Sioux to survive like this and thrive is to have no one power able to exert too much force.
Probably this. It helps they don't have too many resources either, and their land is poor for agriculture. The main value it has is that it's there, so good for ranching and transportation across it.
In the end I think it's inevitable they'd be made a protectorate of some larger power. They don't have enough people, and there would be too many foreign influences there which would cause strife in the ruling classes. At that point, given a "westernized" Sioux, their leaders would have no reason not to go for protectorate status to solidify their power. The autonomous status the Sioux will have will be a good motivator for other indigenous nations who won't be afforded nearly the same treaty rights the Sioux might be able to grab.
Later they might be able to remove the protectorate status, but they'll be pretty poor since unlike the Comanche (who are also cited as a potential surviving Indian state) they don't have a lot of natural resources. I think the Comanche have a better chance of success later on, but not as good of chances at survival in the 19th century due to better land.