Even Russia, who is more than happy to see the West twist in the wind, has said Snowden should stop leaking state secrets, presumably because they also don't want their secrets leaked.

No, they said he should not "harm the US" if he was to get asylum.

As Snowden had already handed his documents to others, presumably Russian authorities knew full well that making that promise would be easy for Snowden and would not make any difference, and it made it easier for Russia to appear to be taking the high road.