I am really sorry you are in physical pain and dealing with the prospect of surgery. I have also become quite depressed from chronic pain before. In addition to the pain itself causing depression, for me personally, I found the actual fact of having a chronic condition to weigh on me psychologically especially if relief seemed far away, including grief at what I lost due to the physical problems, such as not being able to participate in things I once loved, social isolation, etc. So, that kind of thing is something to possibly address in therapy, at least for me.

I can't say what is best for you, but I don't see any reason to not address both if they are connected. If the pain is really severe, though, I could see if being pretty distracting from being able to focus on the mental health side of things in the short term. At least maybe some support as you go through this process from a therapist might be helpful, though?