You are right, but the hard part for me is determining the causality here. Am I depressed because I’m burnt out, or am I feeling burnt out because I’m depressed?
I usually try to avoid engaging in armchair psychology, but "the burnout has penetrated so many facets of my life (various hobbies, etc.)" makes me think it's depression causing the burnout rather than the other way around.
I suspect treatment will be much the same in either case.