I have a type of autoimmune arthritis that took around 5 years to be diagnosed. During that time, my depression got pretty much untreatable with "medication plus therapy".
After the arthritis was diagnosed and I started taking medication to counteract the autoimmune inflammation and dysfunction, my mood slowly improved and I became responsive to antidepressants again.
I also have fibromyalgia and chronic fatigue syndrome, which is an immune-mediated condition. I have found that my mood problems usually get worse when my autoimmune/immune system problems get worse.
Other items on your list that I've had problems with for long periods of time are low vitamin D3 levels, low B-12 levels, and various forms of anemia (oops, that last one wasn't from your list but it definitely seems to affect my mood.)
Another thing that I think is often associated with depression and anxiety is
dysautonomia.
Thanks for this topic. I think it's important to treat and to think about our mood dysfunctions from all fronts, and physiological dysfunction is one that often gets overlooked.