Way back when i was starting my journey into treatment, a bit over two whole years ago (LOL!),i had pretty strong anxiety and depression. OK, extremely strong. Rather than trying to medicate the depression, the generalist psychologist got me into a gender therapy program fairly quickly, where i was started on mindful meditation and weekly talk therapy, individual and group, to help me control this. I went onto HRT after 3 months, a delay I wanted to make sure I needed this and was thinking clearly. The docs would have started me after one session, it turned out.
That is what cleared away much of the depression. The immense calm i felt as the T blocker kicked in was remarkable, and once I started Estradiol the relief felt almost like euphoria.
I bring this up just because, rather than treating depression as a separate issue, i really do think more integrated care, as you hint at, can be beneficial to some of us.
I hope you'll be able to find proper care soon!