Where did my documents and desktop go when logging out of iCloud?
They are synced to the other Apple ID. All information in the iCloud is stored there and logging out of an Apple ID will take all the information away with it.
To retrieve them, I suggest logging back with the ID and copying them to the local machine. Log out, and log into your new Apple ID.
There’s no other way around it. Apple is very strict about information stored in the iCloud