I can't even begin to guess what goals the Russians envision at this point, but it probably involves a drastically weakened Ukraine at the very least, with Russia annexing at least those territories which she currently holds. What Russia can actually achieve is an open question.

The long-term objectives the US seems to be seeking is more concerning from a Chinese point of view, since they obviously want the fall of Putin (with the Russian Federation either broken up or reduced to a Western vassal state). Whether or not this is achievable aside, success would mean China would be almost completely surrounded by hostile powers on most land borders. Some blind ultranationalists in China might even welcome a Russian breakup as an opportunity to regain land Russia seized from Qing, and the US would certainly offer that as a temptation if the Russians were that close to defeat, but it would be geostrategically penny-wise and pound-foolish. Under no circumstances would any Chinese leadership allow such an envelopment by the US. This is not a safe time for China, which the US holds to be its true enemy rather than Russia.