The "OR/SD" metric is somewhat arbitrary. It's just convenient that it is 1 SD; there is no exact reason. If you wanted to make it OR per 2 SDs, you could just multiply the OR by 2.
Imagine you have a distribution from 1st to 100th percentile of PRS, and you have a linear association between percentile of PRS and probability of disease. How would you quantify this? OR/SD is a quick and easily interpretable way to say how sensitive the PRS is. In other words, how "fast" the OR increases as you increase PRS.
The method for obtaining this metric usually involves converting your raw scores into Z-scores. The slope of your regression where Y is OR and X is Z-score I think would correspond to OR/SD.