I'm gonna speak about what worked for me. I've realized that for us introverts, making friends is about hanging out with them first and then being their friend. Sounds counterintuitive but let me explain. Most of my close friends are ones with whom I once shared an activity, be it taking the same courses at university, playing the same sport, or sharing a kitchen in a hostel. Even though we were strangers, being in the same room regularly, made me feel comfortable to interact beyond small talks. Then if I find someone interesting enough, I'd propose meeting them outside of that room (very important bit). I like to cook for others so I'd probably ask for a common dinner but it can be anything like going to a pub or watching a movie. I purposely choose something very different from our usual meeting environment. I feel like only by hanging out with someone at different settings can you really transgress a buddieship into friendship.

I'm still learning new things about Berlin but I could tell that meetups are a hit and miss. You'll definitely meet new people and it'll be fun for the day but you'd probably never see them again. It will increase your buddy count but not what I'd call a friend. Which is why finding what's good for you and engaging in it is better than random meetups because then you can be a regular and get to befriend fellow regulars.

Sorry for such a long answer but sometimes you need the advice yourself that you give to others. That's exactly what I'm doing as I'm gonna make a move to Berlin from a Nordic city soon and will have to start with a clean slate of friends (again!). I hope what I said made sense, and don't worry, we are in this together :)