Why would you say "but economically" in your first sentence?

Is hegemony merely a competition about who can blow up the most people? If you think the Chinese economy doesn't count for anything re force projection because they haven't bombed anyone lately idk what to tell you.

Why doesn't the USA stomp out Russian aggression in Ukraine? Does American force projection only come into play when bombing third world poverty states? Should I thus conclude American hegemony is illusory? Do you think the wars America has prosecuted in the past two decades have made the country stronger?