I'm afraid I'm not T2 and don't recall specific blood sugar problems during my menopause which wasn't bad at all.
I am T1, wasn't carb counting and was eating masses of veg/salad and taking black cohosh tablets (our GP recommended them to my sister when she didn't want HRT and was having problems with her menopause). They helped both of us but it's hard to quantify how much.
Are you the right age to be menopausal, and also showing signs in terms of scanty periods etc? If so, you could well be menopausal but your doctor could confirm for you, and maybe prescribe HRT (if desired) or something else? That might help with your sugar levels. If you don't want HRT there may be something else available now, new drugs come out all the time.