While I cannot say for certain, I think there's something to be said about them both maneuvering to get on the US's good side in the post-cold-war, US total hegemony era of geopolitics.

Russia for its part really wanted to be part of NATO and join with western capitalism, something it was eventually denied and eventually realized it would never get.

China on the other hand still had the US as its largest trading partner and was trying to grow its productive forces and move up the value chain without drawing attention to itself or making itself a target or enemy of the US. To do that not getting in the way of US goals was probably necessary as if they started vetoing things like the old Soviet Union the attention and the anger and attacks on them likely would have started sooner. One can argue endlessly about what they should have done, the impacts, etc, it was simply caution on their part and biding their time while they built their own power and diversified their interests beyond the US and its vassals in Europe.

Basically everyone was letting the US do its thing and there's a good chance we must remember that even without UN approval the US may very well have done many things anyways in the late 2000s/early 2010s in its position as hegemon.