Hegemony is the right word; it means one group dominates.
The russian hegemony keeps you under their thumb w guns; the US & NATO hegemony does it with bondage of many forms.
The US literally armed and funded political violence to ensure the governments we got in the EU and they’re the Jr partners of NATO; Ukraine will have to give up a lot for the same privilege in its future proxy wars w Russia funded by China.
Joining NATO now may look nice on the surface because our standard of living looks impressive; but this empire already started crumbling decades ago and you’re hoping that Ukraine joins the side of the future world’s second biggest world power just as this Roman empire has started to decline.