I'm not sure EU will resent the US. Why do you think so? By that logic Russia will start resenting China and try to decouple real soon. EU needs US for the nuclear umbrella. Their nukes are not enough for MAD equilibrium with Russia.
Also, a weakened Russia that defers to China is actually very good for the West. It is not so great for China posturing either, as China is perceived as standing alone against a unified West.