I think you should just make a habit of talking to people around you. You're kind of putting human interaction on a pedestal and that's just going to make you overthink things.

First of all, you need to understand it's not some pre-planned thing. You should be making a point to go out to do things you like doing - not going out with the explicit agenda of just talking to people. That's why I think the term "cold approach" is loaded, and full of shit--It inaccurately makes it sound like something negative and unnatural--In actuality you've done it many times before without thinking about it.

Seems you've gone deep into this analysis, of which none of it is actually relevant though, because you're not talking about the root cause of your feelings. Which is that you have social anxiety.