A journal to keep track of important information the player has gathered was a planned feature from day 1. However, we completely ran over our time getting core game systems going and it is still on the ToDo list, if we can manage it.
As for the lack of motivation, you are correct that a game needs to give the player a reason to investigate. But our intent in the writing was that "Being Stuck in a Time Loop" itself is itself an existential threat to Mizuchi. We didn't feel any further threat was necessary to get her motivated to action. The movie Groundhog Day is based on the same problem, after all.
Besides that, thanks for playing. I am sad to report KogaBanki was something our cover artist Hippppo just wanted to add and they are not planned inclusions in the game proper. Something about Keine and Mokou, though, you can discover.