Basically, I think the conclusion in that thread is that there is no uniform definition for the deviance from normality, since it can be defined in many ways.
I think most textbooks advise not to use the Shapiro Wilk test anyway and just use a Q-Q plot and inspect the matter graphically. Obviously, that does raise the question how to decide when the data are too non-normal. But in many cases violation of the normality assumption is not that critical, anyway. What is the context for your question?
I read the thread (and again) and they mainly say what is not effect size ...(not W...)
I thought the recommendation is to use a combination of Shapiro-Wilk and QQ plot.
I don't really believe we need to use our eyes instead of the computer ... and I suspect a combination of Shapiro-Wilk test and effect will give a better result than only Shapiro-Wilk test, like in any other test.