@Aurelien_1009
I am prediabetic (but blood sugar in normal range for 2 years) and have never been overweight. (My height and weight were very similar to yours at diagnosis)
When I switched to LCHF I also lost a lot of weight.
I started a food diary and for a period weighed what I ate. I did this initially to work out carbs, but when I was losing weight I also looked at the calories. I was surprised at the low the number of calories I was eating (about 1500 per day). I never felt hungry so my hunger was not a guide to my eating.
When I found this, I looked at foods that would increase my calories without increasing the carbs. These included tree nuts (walnuts, almonds, pecans, brazils, hazelnuts are all relatively low carb and high calorie), salmon, other oily fish, cheese, double cream, eggs, olive oil, avocado etc.(I don't eat meat so that was not open to me).
I found that for me, with the type of food that I eat, I need to eat about 2500 Kcalories to keep a stable weight. If I eat about 3000 Kcalories I put on weight. If I eat about 2000 Kcalories I lose weight.
The only excercise I have done so far is a lot of walking. I managed to regain some weight and have now had a stable weight (+ or - 0.5kg for about 2 years). I weigh myself once a week.
Most people on this site do not find tracking calories to be helpful when trying to lose weight. However I found it helpful when trying to stop losing weight and to put some on.
Since you were diagnosed you appear to have started excercising much more (you say it is using 500Kcal) and eating less. You are probably not eating enough and will need to increase fats and protein. I would suggest taking a typical day, weigh your food and work out how many calories you are eating. You can then see how you can increase this
best of luck
(I don't know anything about vitamin supplements)