That's because most threats to democracy would shift it to being an autocratic, dictatorial republic, rather than say a monarchy

Or to put another way, the risk is in the "Republic" aspects like the Senate and Electoral College overwhelming the "Democracy" aspects like proportional representation and popular vote.

No, "republic" simply means that governance is a public matter, not the private concern of a sovereign. It has more to do with the government's theory of legitimacy than how it is actually governed.

The UK is non-republican because it's governed by Her Majesty's Government, but democratic because the actual power to choose the government belongs to the common people.

The US is republican because the government is constituted by We The People. If it became non-democratic, it would likely remain republican because changing a government's theory of legitimacy is harder than changing how the government actually works.

Your thinking of "union" not "republic"

You stop having a republic when rulers start picking their replacements. You'd lose the republicanism if say, Joe Biden appointed Hunter Biden to be the next president or if it became tradition that the next Trump always gets voted in as president.

Things like democracy and the electoral college tend to protect republicanism, but both can exist without maintaining the republic

Is there a parallel risk of "Democracy" overwhelming the "Republic" aspects of our Democracy*?

Not in the USA, of course, but philosophers of government have identified this as "tyranny of the majority".

Threats to our republic are filed under states rights, a fundamental construct of a republic.

This itself is viewed as a threat to our democracy by those who either think it should not be a republic or are ignorant of the fact it was intended to be. For reference, see debates about a non proportional senate and the power of minority population electoral power.

Many republics (including Singapore) do not have "states", so clearly "states rights" is not "a fundamental construct of a republic".

Nobody sane has ever cared about "states' rights" consistently - it's a silly concerpt. It was invented as part of the Lost Cause mythology to justify secession. (Fugitive slave laws, which are pretty antithetical to 'states rights," were very much something the antebellum South pushed for.)

The distinction is "threat to any government" vs "threats to OUR government"

Sure, ANY Republic does not rely on States, as evidenced by Singapore. But OURS (if you are also a USA citizen) does.

you are correct that I should have stated "our republic" not all republics.

That said, the idea that "states rights" originated after the civil war is absurd on face vale. Powers and autonomy left to the states are evident in our founding documentation, and obviously present in the lead up to the civil war as well.

The idea that a centralized government leaves no powers to the state and local level is a silly concept and counterfactual. It is obvious in the interstate commerce clause and many other parts of the constitution.

That the US started out as a federation of independent states is a given. My point is that "states' rights" as a political-moral philosophy doesn't make much sense, and almost nobody has pushed for states's rights consistently or when it goes against what they otherwise want. One might argue that decisions should be made at the smallest (most local) level that makes sense, but the idea that "state" means "local decision-making" is pretty dubious. Furthermore, "states' rights" as a political rallying cry in the US came after the Civil War and was used to justify segregation.

That’s because they’re the same thing in different languages. I learned the same propaganda as you; the distinction taught to us was basically made up.

Per google search ".. etymology" demos: the people; -cratia: power, rule; Greek. res: entity, concern; publicus: of the people, public; Latin

"Rule of the People" and "Concern of the People" sound SIMILAR, sure!

Just because a mechanic is concerned for your car, does not mean he owns it... I think it's lazy of you to call this dichotomy "propoganda" without offering any definitions or etymology.

English etymology doesn’t get you there and encourages exactly the kind of distinction without a difference that I’m pointing out.

One is Roman. One is Greek. They describe the same concept, but it’s a concept that has been implemented differently both in their time and in ours: self-government. The forms and institutions are distinguishable as “Roman-style” or “Athenian-style”, but the same is true in 2022 of “American-style” and “French-style” republics.

Did Google not give me Greek and Latin etymologies?

Sure it did, but with explanations in English most likely from etymonline.com which, I like the website, but is as much a point of view source as any other. A dictionary is not a source of truth, it’s an editorialized compilation of points of view staffed by people who write the words on the page. The definitions you cited also leave plenty of room for interpretation but the part you want to look at are the mechanics of their society and in particular how power was wielded and the maximum extent of a voter’s power, not a dictionary.

Republic is a type of democracy. You’re thinking of direct democracy when everyone is talking about the form of government where most adults can vote.