> Defining what is a country, let alone a continuous empire is very messy business with a lot of national narrative tied in

It's not that messy, it's just a disagreement about what a "country" is. You're thinking with the European mindset of "nation", where a country is defined by its borders, history, etc. The OP is thinking with the American mindset where the country is defined by its founding documents and legal principles. They're entirely different.

In the latter mindset, Prussia, the German Empire, etc., really have nothing to do with modern Germany, because Germany is not a kingdom or empire, it's a country that was founded in 1945/6 by Allied occupiers. The only messy thing about it is the reunification in the early 1990s, because two formerly separate countries (DDR and BRD), with extremely different systems of government, were stuck together, but under the same system of government as the western side, which really makes it an annexation.