My kids don’t go to sleepovers and never have. I don’t do the school run so no parents invite them for play dates, now they are older parties have dried up only the youngest gets invited now my older kids are too old for “play dates”
You didn't say how old they are. Presumably they have friends who they visit themselves then, if too old for playdates? Or clubs or hobbies they do where they don't need you to chaperone them and hang around? You can join a gym with classes for kids that they go to while you get some time alone, you can use meetup to meet other single parents, I don't understand how you could know literally no other parents with your kids having been to school? I rarely do school runs either because I'm working but you meet other parents at school events or activities and through the school whatsapp groups etc etc.
I get the impression that you are very negative, you make excuses not to try any of the myriad of things people have suggested and you seem to think the solution to all your problems is a man. Whether that was your awful ex or another one, it would undoubted end in tears if you found a relationship without sorting yourself out first, getting out of this incredibly negative mindset and build a life for yourself. What kind of relationship do you think you'd have with anybody when you're so unhappy and refuse every option to make your situation better? If you think a man is the answer to that you are deluding yourself.
What are you doing for work? Focus on that, work for career progression, get some financial stability then funding childcare for more time for yourself or with friends will not be such a problem, make an effort to connect with more people and build some friendships.
Starting any kind of relationship when you're so clearly unhappy with yourself and your own life and have such poor boundaries you think it would be a good idea to move in with a man who walked out on you and your children and doesn't bother with them as it is, would be a disaster.
I don't know why you won't listen when pretty much every poster has told you it's a terrible idea.