It's hard work. I moved to a new city two years ago and put a lot of effort into making friends. If you're the one who doesn't have a friendship group, you're the one who has to do all the asking, which can feel a bit relentless. But in my experience people do respond to it. Most people want to have friends.
I joined two groups - I play bridge at a local bridge club and I'm a Quaker, so go to Meeting on Sundays. IME some groups are better for making friends than others - something like a book group where people talk to each other is better than something like yoga where people just turn up, do yoga, then go home. Pick something that you're genuinely interested in, even if it's something you haven't done for a while as hopefully you'll meet people like you. Once you've been going for a while, you have to be the one who says "Hey, do you fancy a coffee sometime?" Some people won't respond, and you have to make your peace with that. But most people are delighted.
When you're our age, you have to work for friendships, they don't just happen organically.
I have two friends I made in my 20s who were really determined about making friends - they both went straight in and started inviting people to stuff. I found it really inspiring seeing how successful it was. (They both went to private school which I think helped with the confidence thing!)