I believe you can make friends at any age. I don't see why your age would stop you. You've always got the chance to meet someone, at least thats what I think. The most common thing people think of as a social situation after uni is work, so maybe you might make friends at a future job? Or joining local communities/online communities and connecting with people. You could even try reconnecting with your old friends.
As for relationships, there should be no shame for someone having their first relationship at the age of 22, or 35, or 67. There are so many reasons people may not date someone at all or until a later age. I know people can be rude and mean and judgy, but now you should readjust your idea of a good partner, that would be someone who wouldn't shame you for your inexperience and shyness. I know of course reassurance can be drowned out by the anxiety, but anxiety can also be drowned out by the affirmations.
As for repeating the cycle, I think just letting new friends know that you have a busy schedule in life, or that you can't text often. And then when you feel more comfortable with sharing, telling them what's happening in your life will give them an insight to you as a friend and also an understanding as to why you can only meet once a month or text them back so late. Maybe try organising things way in advance so you can carve out some time to set aside for your friends.
At least, this is all just my thinking and opinions. Personally I struggle to message/meet with my friends because of anxious thoughts and so I just kinda avoid the idea all together, which does sound massively rude, but I explain to my friends that I do want to hang out, I just get so nervous bringing it up. We still meet up occasionally, and text sometimes but not as much as I'd like. Its something I'm working on.
Wishing you all the best!