I am just working on my Master's but I have a few friends in PhD programs. One had to get a disability extension, and that might be the answer for you. I think there are laws that prevent discrimination, so you might have to admit to your illness. But they should be required to work around your illness. I don't think you should give up, but don't be afraid to ask for concessions.

Boredom can be a symptom of depression. It might appear like busywork now, but sometimes just slogging it out, you may find some of it coming in handy in the future. And even if not, picking it up later is just much harder.

Remember end of semester is always time for the blues. My daughter was in her Bachelor's and when I would whine about quitting, she was always going into finals and papers, and would remind me that she, and every other student was in the same boat this time of the semester.

My advice is don't give up. How much longer do you have to complete the degree? Would it be an advantage to your career to have this degree now? Would it disadvantage you NOT to have it in the future? Hope you figure this out. Don't question yourself and your goals. Question the depression instead, and you may find the answers you are looking for.