As someone with mild social anxiety, the thought of doing something like that is utterly alien, even in my own country let alone somewhere else. I don't mean in a "i wouldn't do that" sort of way, but in an "i cannot even imagine/does not compute" sort of way.
I also have/had mild social anxiety. When things open up go stay for a couple days in a hostel somewhere (use hostelworld), make sure to find one with a reasonably large common room and be in it, read a book or do some work. It will probably be therapeutic. Not much is forced and socialness tends to just happen. If someone sits near you or says hi ask "Where are you from? How long are you here? What have you done here?" and roll with it. If you do some research on whats in the area or cool food you want to try, you have an immediate opportunity to invite someone to do an activity. It will feel like sitting on an airplane with the door open to go sky diving to you, exhilirating if you manage to make yourself do it.
A useful psychological hack: you have a bit of a desire to do this, hell, it's scary, right? So invite a friend and make it your goal to plan lots of things - its easier to do do something for others quite a lot of the time.
Be explict you are doing this. You'll probably find there are some great bits, some other bits you cant control that are exhausting, etc.
Then do another trip. Plan to invite that friend. Plan for the good bits and to avoid the worst bits. Then just go by yourself!
The first run through gives you a motivation to do something challenging and consider what you would think people want to do, even if its awks.
The second, you take the learnings and reward yourself
I have mild social anxiety. Maybe more than mild. I have to say sometimes it is easier to be social in another setting. For example, in hostels the expectation is to just start talking for no reason and tell that lone traveler that you are indeed exploring the city and inviting them to join you.
Another thing I've found is taking a class - in my case kickboxing classes led to quite a few new friends.
I don't have as much courage to do that in my home country.
Anyhow, good on you for living life :)