You have done exceptionally well, your results were not believed because "they" are used to progressing people onto more drug therapy.
Carbs are not required for even heavy gym work. They are good for a muscle pump as they hold more water and provide the full look - by taking salt before a workout a similar effect can be had (and just a focused hard workout). Whilst it is not possible to give you direct advice like your diabetes dietitian, I can say what I have seen and what I would do in your position, so here's my take:
130 grams of carbs is what the mainstream class as lowest of low carb, due to out dated beliefs on what levels of glucose are required by the brain to function. Many low carb / keto "experts" and participants range from 10 - 100 grams. History has shown that many easily thrive on 10 times less than the 130 grams, but to stay with the science, Dr Eric Westman recommends less than or equal to 20 grams of carbs total and Virta Health are at 30 grams - both are authoritative practices approved for insurance use in the US (I operate between around 20 and 75, depending on if I opt for vegetables with meals and the amount of berries consumed.
Your liver will automatically produce glucose on demand to fuel workouts or general energy requirements. The more fat adapted you become, by having minimal carbs, the easier ketones can be used to fuel your activities seamlessly. I had Covid 4 months ago and have eaten meals like the below to get me back to 7 miles of walking a day and 2 hiit resistance weight training sessions or similar:
Breakfast:
Air fried kippers and nandos seasoned turkey breasts, with berries and roasted nuts with melted 100% Montezuma dark chocolate with chili powder
Dinner:
Fajita spicy chicken and vegetables, tinned sardines, smoked salmon and dry fried halloumi, with a dessert of keto almond lemon drizzle cake (was my daughter birthday yesterday....yes I did a quarter (5.2 post prandial reading, so I will be close to 4 fbg in the morning).
My breakfast is representative, but I tend to normally have home made seed crackers (diet doctor recipe) with marmite for afters and the same nut and dark chocolate or seconds of the dinner.