I understand, these were just loose questions from me ;) I think I have a certain bug, I can no longer get to the fourth floor. The green arrow has disappeared, even though you can see that there are stairs. Without it, I think it will be hard to continue to develop the main story. I also watched this anime, I know more or less what should be next, but I guess I'll have to get to the fifth floor for the story to move forward. The bug occurred while Hestia was at the party of the gods. I may have caused it with something myself, but I don't know what exactly.
When you are in the HUB (where you can pick the location to go to), you can click on the protagonist's sprite to print the current objective. You can also check the Journal for your current quest. If I recall correctly, you need to wait until Hestia is back, and Bell is not allowed past the fourth floor. To progress with the days, the "zzz" icon should be interactable.
You can choose to grind a bit (both for stats and money to buy items) since there'll be your first boss fight soon after.