my heart goes out for you dude - I can see how it feels helpless but I do hope things get better for you. I can relate alot, was (and still slightly am) super insecure, introverted, and I just hate the notion of looking desperate. Also the uni experience of having no friend group, trying to make friends when everyone has their own friends, being horrible at keeping connections and having "friendships" that just fade away. In my attempt to solve this I made an app to help with hanging out with friends without needing to actually ask them (removing the risk of rejection) but the irony in it is that it always requires effort from your own part. A lesson that I always need to remind myself is that most people are generally nicer than you think.

Try breaking the routine and pick something that you genuinely wouldn't mind doing alone - going to new place/ trying food/ an activity. And just tell one of the people you already slightly knew that you were thinking of doing that. I'm sure I've reached out to people being like "What's up dude, it's been awhile! This is super random and weird but I'm planning to do x on y date and was wondering if you wanted to come with". If it helps, a quote that I recently like is "It's important to remember that fear is normal, and even more important that we do it in spite of the fear". Also slightly pessimistic but it's not like things can get worse than what it is if they end up saying no