This is a bit meta but....
I wasn't born a people person. I struggled to make friends until my late 20s rolled around. Very shy. Very anxious. It would stop me from doing things I wanted to. Still there, but I manage it far better.
What changed? Hm. I got into new things. Many things. It was always gradual. But I progressively dropped layers of shame and embarrassment along the way. Now I'm eager to do something that makes me look foolish if I think it is fun.
First thing I would say, is messing up something as an adult is far less embarrassing than as a child. The people around you might tease you, but in general, I would say people are interested in teaching you if you express an interest in learning. So starting new things is far less scary. Most people I interact with have enough opportunity to acquire social status without needing to be awful to others. Humility and laughing at failure is valuable.
Once you begin to overcome that, then trying new things becomes easier. I don't mean, trying new thing as in going to some event. I mean join a club or group, which operates on a schedule. The journey to acquiring some level of mastery will lead you to meeting others at the same level. Those are great candidates for making friends. You already have a common interest, a reason to see each other regularly and you can make a somewhat informed decision over time.
Best way to promote an acquaintance to a friend is to feed them. I prefer dinner/snacks that I make myself (homemade + vegan == very cheap, in general, even if you are feeding several), followed up by a board game. 4-5 people is the best number for this strategy IMO. If you struggle with conversation, best bring along your most social friends and leverage their power of filling in the void. Everyone leaves feeling great, and it happens again.
I think it is common for many people to rely upon a small number of social organizers in their circle. If you become that organizer, then you become the one who summons friends. Then you can decide how much socialization you want
. Just don't get discouraged when every single one of them happens to be busy -- it happens, and you just try again later.
I think many people don't make new friends as they get older. This is a mistake. Don't spend down the social capital you built up as a child. As people move, change, or die, they leave gaps. You need to fill those gaps! Always easier to make friends when you have some friends already. You can introduce people to each other, and if they get along, the common bonds will help keep everyone together for a little bit longer.
.
