It might not necessarily be high in fat - it's probably the calorie restriction that works, as in this trial:
https://www.nhs.uk/news/diabetes/radical-low-calorie-diet-ma...
https://www.nhs.uk/news/diabetes/radical-low-calorie-diet-ma...
Personally, and anecdotally, I have tried calorie restriction dozens of times since childhood and it has never brought down my A1C.
[1] https://asset.jmir.pub/assets/a2c0047f60bd77156d22029b8bdd5c...