There seems to be a bit of confusion in your chat about how Beatrice remembers Subaru. There's no big secret to it (like having something to do with the library) and it's not even some big spoiler: it's a failure to understand the timeline of events - Beatrice met Subaru (and pulled her prank on him) before the reset point, and only remembers him up to that point.
And I already know people are going to ask "but how does Beatrice know about Subaru breaking through her Door Crossing - that's a detail from the previous loop?" Once again - it happened when Subaru first met Beatrice before the reset point. Beatrice even admits that it happened 3-4 hours before this point they're talking now. Beatrice doesn't remember anything from the previous loop that happened after the reset point.