If I grant OAuth access to "Library Card", I will apparently share my e-mail address with it. I'm obviously fine with one WMF project seeing the e-mail address I use on another WMF project, but does this mean my e-mail address is shared with The Wikipedia Library partner companies? What other info is shared with these companies? The privacy policy link only leads to the general WMF privacy policy.
Topic on Help talk:OAuth
This is a question specific to the particular OAuth Application and not the general OAuth service. It can only be answered by someone with knowledge of the application itself. I believe that the "Data Retention and Handling" section https://wikipedialibrary.wmflabs.org/terms/ covers your question, but I encourage you to contact the project directly if you have further concerns.