Impeachment is not a coup.
A coup is the overthrow of the government using illegitimate means.
Impeachment is not an illegitimate means because it is explicitly provided for in the Constitution.
Trump is not the government, but only a portion of it.
Impeachment does not even change party control of that portion of the government.
Impeachment is, unfortunately, seen as a nuclear option, as a very big deal, and is seen as such in part because we are too attached to particular men in office, viewing them as saviour figures.
As a democratic republican people, we should have no such overwhelming commitment to any person in authority.
Our commitment should be to the constitutional system, and any person should be seen as expendable, their removal as a regular business detail done perfunctorily, and viewed not as a threat to the system but as the strength of the system.