Must I offer expiation for an oath, and how many times, if I do not recall whether I swore to repeat the prayer or not, especially given my suffering from obsessive doubts regarding repeating prayers and verifying purity after prayer?

Whispers (Waswasa) are a serious disease that must be guarded against and turned away from. If you doubt that something exited after prayer, your prayer is valid, and the default is that it exited afterward, so do not repeat the prayer. If you took an oath or broke it under the influence of whispers, there is no expiation for you. And if you doubt whether you took an oath or not, the default is that you did not take an oath. Ignoring whispers is Allah's ruling, which He loves for you to do.