There are two basic types of diabetes.
Type 1 is partly inherited (genetics play a role), and then triggered by an infection. At this point it becomes an autoimmune disorder with the body's infection fighting cells attacking the insulin-producing beta cells in the pancreas. The onset of type 1 diabetes is unrelated to lifestyle, so stress and diet do not play a role in its cause. This form of diabetes requires the use of supplemental insulin.
Type 2 also has a genetic trait, but with this form of diabetes, lifestyle factors do play a role. Those lifestyle factors include obesity, lack of physical activity, poor diet, and stress. So, you can see how a person suffering with anxiety/depression would be under stress, might not be physically active (doesn't exercise), and has poor dietary habits.
A person with a rare panic attack may not be harmed by their occasional symptoms, but chronic anxiety is not a harmless condition. It places the body under continuous stress and that can be linked to at least increases in many physical illness.
Even those with anxiety/depression can do so much to help themselves, thus limiting their stress and diminishing their chances of illness such as Type 2 diabetes.
The very best to you, Paws!... Chuck