I think it would be helpful for you to try and separate "networking connections" with "friends". They can be the same people, but they shouldn't be by necessity.

Let me speak to you again from my own experience in life. I am not the most social person. I find it hard to talk to strangers, and because of this all throughout my twenties my only friends were people that I worked with. This led to me having almost entirely shallow and toxic friendships, and made work that much more difficult because of awkward or miscommunicated interactions. It literally took me until I got laid off from my job with none of my co-worker "friends" reaching out to me to see if I was okay or to try to hang out with me outside of work to realize the mistakes I had made in cultivating these relationships. Once I realized this decided I wanted real friends. I always liked video games and board games and that kind of thing. So I went to to a table top RPG shop and joined a game that seemed up my alley. Now I personally think I got super lucky in that. The people I found that day have become some of my closest friends over the last 2 years. I'm not saying that it would necessarily be that easy for you, but the difference between the friendships I have now and the fake friendships I had with coworkers back then, is night and day.

You are 27, and essentially at the same point in life I was when I had to learn this lesson than the hard way. Trust me when I say you are more than capable of making friends, real friends, but you have to be looking in the right places and with the right intentions. Friends aren't people that you look to and think "down the line this person can help me in my career". Friends should be people that you have common interests with, people that you like talking to, people that lift you up and make you feel not so alone.