The metaphor was the part you were being a pedant about.
the LLMs actually stand by their principles much better than fascists
If the audience knows how LLMs work internally, then they know they don't have "loyalty," just stochastic processes. If the audience didn't know that, your pithy "aktually that's incorrect" wouldn't teach them anything correct, but would cause confusion because it sounds like you're denying the metaphor.
Also, it's not an ad hominem to say that you are acting like an LLM: with poor reading comprehension and an overly-literal interpretation. That's an observation of your unproductive behavior. An ad hominem would be insulting you or name-calling with unrelated info, such as calling you "stupid like an LLM."
It isn't a logical fallacy to be called out on your bullshit, even if it hurts your feelings.