How can one reconcile the conditions of repentance related to restoring rights to their owners—and the resulting transfer of good deeds—with the multitude of bad actions and the inability to remember their owners? What is the formula for seeking forgiveness in this case? And how can one absolve themselves of taking a simple item from a library without the owner's knowledge?

Your thought that Allah will not forgive you is a bad presumption about Him, the Almighty, for Allah forgives sins, no matter how great, to whoever repents with a sincere repentance. Repentance is obligatory immediately, and abandoning it is a sin that requires repentance. Sincere repentance does not remove the reward for good deeds. If anyone has rights over you, you must restore them or seek their forgiveness. Repentance is completed by restoring rights. Forgiveness can be sought from someone who was wronged in general terms, and some scholars do not see the necessity of seeking forgiveness for backbiting, and that seeking forgiveness for the one who was backbitten and mentioning him in a good light is sufficient. As for the form of seeking forgiveness, it is broad, such as "O Allah, forgive so-and-so." The value of the ball that was taken without its owner's knowledge must be returned to him without informing him of what actually happened.