I think it's good that you are self-aware regarding depression and anxiety. I also have been diagnosed with depression, and thanks to medication, I feel like I'm on a pretty even keel most of the time.
I want to share my (limited) experience with hospice/end-of-life care. In nursing school
I always said I did NOT want to do hospice nursing, but in my current area (pulmonary/medical intermediate care) I have had to take care of hospice patients on occasion. Usually these patients are people who have recently made the decision for comfort measures only. It can be very sad and emotional. But as you also pointed out, it can be very rewarding. For me, it's one of the few chances I get to really get to know my patient and his or her family, as well as what's important to them, and what I can do for them as a family unit to make this time as comfortable as possible. It's a time when I can focus on talking to and educating patients and families instead of focusing on fixing their problems. It turns out that I'm actually pretty good at the talking/educating part of nursing, so I really like that aspect of it. It also turns out that I don't hate doing end-of-life/comfort care at all. I still don't think it's what I want to do in the long term, but I could see doing it either on a per diem or short-term basis. At the end of my days caring for these patients, I didn't feel sad and depressed as I expected to. I felt like I had made a difference.
And isn't that what we went into nursing to do?
What's my point, you ask? Maybe hospice nursing is your niche. If you spend most of your time feeling like the work you do is rewarding, and you feel like you're able to connect with patients and families, then it probably is. To paraphrase Oceansunset in the previous post: loving your job = decreased depression/anxiety.
Best of luck to you!