I think it is hard when people are so busy just surviving the day to day in their own lives.
I do have some good friends but one has recently moved away and another is struggling with really serious illness. Of course I'm supporting her when I can but she is much more limited in what she can cope with socially.
I use ChatGPT too sometimes but find that it actually irritated me after a while as it starts to try and sum everything up in neat little platitudes. It is also, I've realised a bit of an echo chamber personality wise and you end up messaging yourself but with better spelling!
So, my plan is slowly to join things that I might enjoy/meet people at. I think if you enjoy something you naturally talk about that thing you have in common with others and it helps you connect. For me this might be a creative writing group or a choir.
Could you join an adult education class in something you are interested in? Then you can chat about that thing with others that go. You mentioned religion. I attend a service and coffee morning at a church ( it is midweek, but I'm retired) and have found in getting to know a few people there and the routine of it being every week is helpful in knowing I will have contact with the same people each week.
I understand what you mean about not being too needy, I think.
However, it might be helpful if you did a bit of thinking around what you do need/ want. Then you might have more idea of how to meet that need.
You say you are meeting up with current friends about once a month and that you would like it to be more than that but they don't seem to want that. So, do you need more friends to meet at the same kind of interval so you have more meet ups a month or so you want a deeper friendship to discuss more personal things with? Or maybe both?
I'd keep the friendships going that you do have at the level that seems ok for them. Don't assume that just because you are always the one to arrange the meet up, that they don't want to meet. Some people just aren't very organised or are so busy firefighting the next few days that they can't think ahead. Others may be even more worried about being needy than you are so wait for someone else to broach things.
If you have the time and energy, then I think volunteering for a cause/issue/ task you feel passionate about can help you connect with others. I love little kids, don't have any myself but help friends with theirs as a kind of honorary grandma. This helps my friends who are pretty stretched, I get to know them better and also get to enjoy their children who make me laugh a lot!
I don't have any massive " this is the answer" solutions as I'm still thinking this through myself.
I heard a sermon this morning where the preacher said the place to serve ( which is a really good way of forging deep relationships with others) is where your deepest joy meets the deepest needs of the world. I'm not sure what that means for me but it is something I'm wondering and thinking about.