Something somewhere in the training pipe has perturbed the LLM in a way that makes it say "honestly" all the time. It's a weasel word. It's a habit. It's an addiction. It's borderline involuntary. Even changing the system prompt only makes it 30% less common - like trying, and failing, to break a habit with sheer willpower.
They'll probably change the training pipeline at some point in the future, to banish this habit, but honestly? It's such a low priority that they might take a while getting to it.