In the Records Hall, you can view, well, records! With the Compatibility feature, you can visit the Rainbow Sage to see humorous and randomly generated secrets and feelings between two characters! This is purely for fun and has no relation to the main story. In the Library, you can view Ancient Texts that explain the Lore, which you will have to decipher with their alphabet or the internet, as well as the Unit Roster, which tells you more about each unit’s personality!
In the Theater, you can rewatch animated cutscenes or listen to music. The higher level your Records Hall is, the more music you can listen to. Finally, you can re-read old support conversations in Support Log. Support Log history is saved the minute you view them, so if you view an S rank support scene, then reset your game without saving, the log will still be in there! This way, you can theoretically view and store all the marriage support conversations in one playthrough!