Exactly which party is imposing "authoritarian edicts" on the populace?Actually, either of those is more than adequate by themselves as you can see from the above definitions. Until recently, no one had a problem referring to our system of government of as a democracy as it was understood to be shorthand for representative democracy. I don't believe anybody is under the illusion the US uses the Athenian Assembly model of democracy. Certainly not at the national or state level. And when referred to as a republic, it is understood to be representative republic with popularly elected representatives. The two words have been used interchangeably since before the Constitution was written.
But then the GOP decided it needed to diminish the importance of our democratic institutions in order to impose their vision of a more authoritarian state. Hence the attack on the word democracy. Hence this silly debate about how to describe the federal and state governments.
If we are going to be pedantic about it, republic simply means the head of state is not a monarch. But it in general usage, it is assumed to be referring a representative republic where power is held by the people and exercised through their representatives (usually popularly elected, but not always). Additionally, the powers of the representatives in the US are (nominally) restricted by the Constitution. So a more properly prescriptive description would be a constitutional representative democracy or, if you must, a constitutional democratic republic.
But really, you can just call it a democracy. Unless you have a non-democratic, authoritarian political agenda you are trying to push.
To be more precise we are a Federal Republic with, as originally conceived, the States retaining the greater power. Further it is the states that elect the president the fact that the states have designed their election processes on a democratic model.