I relate very much to this. I have autism and in-person social interactions have been challenging at times to understand. So, I became a student of the human social experience and read a bunch of books about how to speak human, which I think indeed sometimes were more for extroverts.
I have been learning how to gracefully interrupt, how to start conversations, how to have an opinion that is different from the others in the group, etc.
Though in the process I learned a lot about how many peoples' minds work, so that's been useful still.
Why do you want to measure it? If you feel you are improving, that's good enough in personal life.
Also, sometimes, the improvement is just so great (or paraphrased, the baseline is so low), that you don't need scientific rigor to see that things got better.
There are some baseline metrics that are obvious right?
For example, if you have 0 conversations in a given week on average, then having 1 or 2 neutral conversations per week already feels like something better. Why? The goal is now to make those conversations feel slightly positive.
You don't need to prove your success to anyone else, so scientific rigorousness isn't needed. What's needed is your own evaluation of how things are going based on metrics you find important. The metric I gave is just an example, there are many metrics one could choose from. It really depends on the outcome you want.
I have been learning how to gracefully interrupt, how to start conversations, how to have an opinion that is different from the others in the group, etc.
Though in the process I learned a lot about how many peoples' minds work, so that's been useful still.