Except Chinese hegemony is illusory beyond what it considers its immediate sphere of influence which also means it really cannot project force in any way but economically. It can barely take care of business at home. It's puzzling to many as to why America sees China as somehow equal in threat and in capability since in reality neither is remotely true. China doesn't even have a policy that is truly expansionary since Taiwan is an irredentist claim. Its armed forces have not seen combat since 1979 and that was largely a ground war. Without connections or having acquired one previously it's becoming difficult to obtain a passport to leave, although, it's also not all that easy to find a place for you to settle as a Chinese citizen without some sort of skills that allow you to pretend like society under you is unstable.
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?