I enjoyed reading what you write here. A few years ago, I had a condition where I suffered greatly from the fact that I did not have friends. I have a couple of people that I can talk to, but this happens quite rarely. And I realized that I should learn to entertain myself. There is nothing wrong with going to a cafe to eat alone. Doing sports without anyone also turned out to be great. I really liked the idea of team sports. And you know, when I stopped worrying about the fact that I had no one to communicate with, I became more interesting to others.I definitely empathize with what you are writing. There were several years when I essentially did nothing except hang out on YouTube after school. I did practice badminton and table tennis which was a lot of fun, and it was important to be physically active, but I also didn't really connect with the other kids so I understand your worries regarding being "the weird one". I have a few suggestions you might find helpful.
1. It's late in Switzerland now, so you won't be able to contact any of those groups now. However, I want you to write yourself an email, adjust the sending settings so that you receive it tomorrow after work. In this letter I want you to write the phone number or email address of the places you are interested in, and a command like "call them now". I find it much easier to do things if someone is telling me clearly what to do, so that's what I'm doing with you now. Don't postpone. Send and then contact. You will feel relief of having accomplished the call and started something new, even though it's a difficult wall to push through. I believe you can do it .
2. Set yourself tasks. I'm not talking about something generic like "make more friends" and "be more social". Maybe that's what your end goals are, but it isn't useful for you to think about now. What I'm thinking about are smaller identifiable steps which can increase confidence in yourself.
One of the goals I set myself was to learn the names of people going to university with me. I had always been really terrible with names and didn't even learn the names of the classmates I had been with for 7 years in elementary school till the last year. However, when I thought about it, I realized that the reason I didn't remember any names is because I didn't really care about the people, so I didn't even try to memorize them. Remembering anyone's names didn't gain me any friends directly, but it did help me be more confident in social situations, even though I sometimes had to ask a person their name 5 or 6 times. It also meant that I was "seen" as more friendly, so people felt better about talking with me.
Your task can be something like "apply to a social event" (like badminton or a theatre troupe ), initiate sending a message to someone once a month (can even be on the forum), or "excuse myself and go somewhere private immediately when I find anxiety kicking in instead of allowing it to build up and overwhelm me". Those goals should not feel impossible or damaging to you, and there should be clear benefit (increase social skills, better emotional self-regulation). You should not feel bad for failing the tasks, but it should rather be things you can always work on and feel accomplished about when you feel like it. At other times it's just not something you feel comfortable doing, and that's okay. It means that you might need smaller tasks or that you are going through a rough period. It happens.
3. Be patient, and don't put too much pressure on yourself. Remember that though they can be worked on, social skills tend to be biologically more difficult for people on the autism spectrum to learn due to sensory overload. It's perfectly normal to have difficulties connecting and feel like the odd one out. I can tell you that from my own experience, I've only once been a part of a large group, and that was due to very unusual circumstances I doubt I'll encounter again. I've taken acting courses, practiced badminton and table tennis, with joola, volunteered and even joined a choir. None of those activities gave me a friend and I always felt like the odd one, but I persevere. The reason I do so is not because I am still wishing to find a friend, but because I enjoy the activities. When I have found friends, it has always tended to be other loners or outsiders, so I think that's what you should look for. If you see someone awkward and by themselves, try talking with them. They might feel exactly the same as you but didn't want to risk awkwardness (just like yourself). Being more active has really helped me be more confident in myself, and I hope it can help you too.
I don't have specific suggestions for how far or often you should travel. As @Angular Chap mentioned, that's for you to decide based on what you know about yourself. I wish you the best on working at strengthening yourself. I know it isn't easy, and can in fact be very difficult. I think you show great strength in writing this (and other) message since it can be scary to open oneself up. However, I've really enjoyed your presence on the forums, and I say it in full honesty from what I know of you based on your messages that you can do it.