Is it possible to rearrange the sidebar that contains the different folders representing rooms and objects and such?

For example, say I have a room named Bedroom, and below that is a room named Kitcen. If I wanted to add a room named Hallway, it would be put at the bottom of the list. Would there be a way for me to move it under Bedroom and above Kitchen?

Seems like something that would be obvious, but so far, all I seem to be able to do is move rooms into another room's folder, which is not at all what I want.
I'm trying to organize my game because it's getting pretty messy.

There is nothing built-in. There are a couple of approaches that you can try.

Create new rooms that are zones or chapters, and put all your existing rooms inside them. You can collapse any you are not working on, and just focus on the one bit. Note that when you add a new item to a room in a zone you will be asked if you want it to go in the room or zone, and it will default to the zone.

If using the desktop editor, open up your game in a text editor (back it up first!), and move the rooms around there. I would advise using Notepad++, and telling it the language is XML, then you can collapse each room, making it easier to ensure you move the whole thing.