Want to start blank project and transfer old into it. What problems can I expect?

So my current project is cluttered. Really no single hierarchy and it’s hard to find stuff.

I want to start new project, set up hierarchy of folders then transfer stuff from old project into this one, such as textures, models, scenes, prefabs.

What should I be careful of and what problems can I expect?

I would recommend actually not transferring to a new project. That won’t really solve anything that you can’t solve in you already existing game project. Also There is nothing preventing you from getting into another hot mess with organization in a new project. It would be best to just organize what is already working. You should actually save time that way, because you won’t have problems were you missed importing something properly and you are just doing the same work that you will have to do anyway. I would recommend backing up the original working project and doing this to one of the copies of course.