Hi and welcome to the forums. I also have (had) the gout and T2 problem. Gout in both big toe joints. My experience has been that my gout vanished since I got my blood glucose levels back to normal. Before that (ie 2019 and back) it was managed by using naproxen and codeine.
I have found zero association between the usual suspects for gout (purines from meat, wine, shellfish, alcohol etc) and what was happening. It's therefore not been a problem to manage diet, as no management was needed. I eat around 20g carb/day, lots of meat and fats, a fair amount of alcohol, shellfish, that sort of thing.
I suspect that what was happening with me was that, because the T2 affected my kidney functions, I wasn't urinating very often. I was therefore not getting rid of uric acid and was getting build-up. Now that my BGs have neen normal for getting on three years, and my kidneys are functioning properly, I'm not getting any uric acid build-up, no crystallising and therefore no inflammation or pain.
I found this link helpful:
Gout is a form of arthritis, causing intensely painful, red, hot and swollen joints (often the big toe). Learn about the causes, symptoms and treatments.
www.versusarthritis.org
Best of luck. Hope this helps. Gout is awful to live with.