The way I understand empire is a state which tries to expand its influence and dominate wherever it can.
And yes, for people being dominated by it, it has a negative connotation.
Different from a democracy and federation.
Because a democracy fighting for freedom and ... well democracy, would not do this:
https://en.m.wikipedia.org/wiki/United_States_involvement_in...
"During the Cold War in particular, the U.S. government secretly supported military coups that overthrew democratically elected governments in Iran in 1953, Guatemala in 1954, the Congo in 1960, Brazil in 1964 and Chile in 1973. "
This is what empires do.
Dominating their way onto weaker states, by all means. Sanctions, assasinations, supporting, supressing, blocking, sending weapons and ultimatively troops. There is a reason why there are US bases all over the world.
And yes, sometimes that can be a net gain, like in Nazi Germany, but usually all the human rights democracy talk is just facade.
And also yes, smaller states do the same, act like empires, but the US is by far the largest Power since the USSR vanished.
But china is on the rise and europe likes to be an empire as well ... but for example with europe I have the hope that we tend to stay more a democratic federation and not go down that path as well.