All communication takes place directly between your smartphone and your library's server. We do not save any data because we do not get any to see. Neither your search queries nor your account data – everything is exclusively saved on your device. We do not know what data your library's server saves – you would need to ask your library about that.
Only exception: When you share a search result from the app to your friends, the link that your friend saves takes a detour through our server (if he does not have the app installed and set-up for the same library). In this case, our server will save the time of the request and which book was requested, but no IP addresses, browser data etc. This is necessary because this "Sharing" feature is something that most library systems do not support natively, so we need to rebuild it using this technique.