A low carbohydrate anti inflammatory diet can certainly reduce blood pressure and blood glucose, but I think HbA1c is more of a surrogate marker. My understanding of hypertension is that it’s part of metabolic syndrome just like diabetes. Confounding factors.
I believe the primary mechanism is thought to be narrowing of the arteries necessitating that the heart beats harder in order to move the blood around your body. Narrowing of the arteries will be alleviated by the same diet that alleviates high blood glucose.