First of all, happy belated birthday, OP. I'm so sorry that everything looks bleak to you, and I completely get that 'nothing ever works' feeling. I've been there often, and I could have written lots of your post when I was in my mid-30s.
Someone upthread asked what your 46-year-old self would say to your 36-year-old self. Well, I'm a bit older than that (early 50s) and I know what I'd say to my 36-year-old self who I think felt some similar things to you.
Number one, stop worrying about being fat. Most of the rest of the world doesn't care what size you are, and being overweight emphatically doesn't make you a bad person. It took me decades years to begin work this one out, and there was a lot of wasted shame and embarrassment, and opportunities not taken, along the way.
Second, don't try to change the whole of your life. Just start to do one or two small things that give you some enjoyment, and enjoy them while they're happening rather than spoiling them for yourself by thinking about how shit it's going to be at work tomorrow, or how you're going to go back to an empty house. For me it was going for walks, quite short ones at first, and joining a community choir. For you it might be other things, you might have to try out a few. Eventually they led on to going on real, proper country walks and walking holidays, and joining an auditioned choir, but not until I'd built up quite a lot more confidence than I'd had at first.
Third, mid-30s is by no means too late to re-train for work that you'd find more rewarding. I did horrible, insecure badly-paid (pre-NMW) jobs through my 20s and early 30s, and I know how bad that can be not just for your standard of living but also for your sense of self-worth, especially if there's no partner in your life bolstering you up. It's damn hard from there to make yourself feel like you're worth investing in, but start looking at what's out there. Have a look at job ads for things you might want to do, and see what qualifications you would need as a starting point. If you're able to say on this thread what interests you work-wise, I bet you'd find some MNers in that field who could give you some pointers. With retirement age retreating into the late 60s and possibly later you've got a long working future ahead of you, and now's as good a time as any to start planning for it. In fact it's an ideal time.
I also completely get not believing that your GP or counselling will help. I don't know you and I don't know your situation so I wouldn't presume to give advice on what is after all a medical matter - just to say it might be worth giving it a go. If it doesn't help, you haven't lost anything. If it does help, that's an unexpected bonus.
I'm sorry if any of the above seems trite or dismissive. There's nothing like a bad birthday to make you (anyone) feel truly awful, I know that. But it really, really doesn't have to be the story of the rest of your life.