More specifically it's an auto-coup; some political figure gets into the power through legal and democratic means, but then gets rid of that political structure so they can stay in power indefinitely.
A good historical example of auto-coup is Nazi Germany. Hitler tried a "plain" coup in 1923 (the Beer Hall Putsch), but it failed, and he ended in jail. His ascension to power was instead by being elected chancellor / Kanzler of the Weimar Republic, and then creating a "think on the people!!!" edict. Except that the edict gave him the rights to create and enact laws without the approval of the parliament / Reichstag.
The key difference that I see between Nazi Germany and its spiritual successor is that the "leader" of the successor isn't its actual leader. It's simply too easy to manipulate an idiot who thinks to be powerful, and has an ego bigger than the brain. 2025 USA differs from 1933 Germany in this aspect; it's like if Goebbels was the one actually in power, with Hitler as a simple puppet.