You keep saying I won't meet a partner, I won't have children, perhaps you won't have children, but given you have about forty years left of your life, the chances of not meeting a partner, if you want one, and want to go to groups like walking groups, MeetUp and so forth, is quite low. My mum, gran and other gran have all had second and third relationships into their sixties and seventies.
Can you not see your 'it's all over' mentality at 36 is just a product of depression, and not actual reality?
I can't suggest what that thing is that is going to turn things around- it could be volunteering with children, or abroad, or taking a singles holiday, or doing online CBT or whatever- but there are a huge number of options, too many to list in fact, and I know whatever I suggest you'll say- I can't do that.
That way of thinking, borne of depression, is your problem, not the lack of productive ways to spend your life, or indeed the lack of nice people out there who want new friends and partners (and whatever you say it isn't all about looks as a quick look around any town centre at the couples holding hands will tell you).
I think you need help for depression, have you been to the drs? Have you thought about self-help? (if not exercise, something else perhaps online), counselling (perhaps getting a discount if not got much money) and so forth. Or posting in mental health on here and getting better advice from people who have experienced it?
You don't give a lot away about your life, and although that is self-protective it makes it hard to advise you, as I don't know what you like to do/what qualities you have/what skills you have (except teaching and writing nicely!) I don't mean you have to disclose everything if you don't want, but it does mean the hit rate of sensible suggestions will be lower.