myfirstandlast -- I can give one simple reason to why bother cleaning the squalor ... it will help some of the depression. Don't try to do it all at once. Don't even try to do one room at once. Do a little at a time. I know, I've been there. Pick a table, a corner, a chair. Get it cleaned up and then put something there so that it can't get cluttered again (I actually put a live plant on a chair so that I couldn't dump anything else on it).
The next week, pick a different spot in the same room. It really is okay to take a week or two to clean one spot -- just make sure to find a way to keep it clean once you've got it done. Keep working on that room until it is done.
It may take you a year (it did me), but you will end up with a house that you can live in and not make you want to sit down and cry every time you walk through it. If you have a friend who can help you, grab that friend. Again, I did. It killed my pride but it really did help in the long run.
Depression stinks. Depression and ADHD combined are nasty. been there done that and, at times, still doing it. Oddly, one thing I'm doing now when I feel the depression coming is forcing myself to clean my room. It really does make a difference when you can enjoy your nest. My bedroom is mine.
Baby steps work wonders. I truly am speaking with the voice of experience here. I didn't even know how much my slop depressed me until it was gone. I'm still prone to bouts of depression but they're different now. Go away quicker. I'm more able to cope, not just lie in bed and try to turn my back to the world. Even while depressed, I can go out and do things and truly laugh. The more I do, the more I laugh, the better things are. Having a home I could live in, not just survive was truly the beginning for me.