Moving a Folder
Open the overflow menu (⋯) on the folder row you want to move.
Select Move. A folder picker opens showing your folder tree, with the folder's current parent pre-selected.
Choose the new destination - this can be another folder or All chats.
Click on Move.
You will get a toast notification confirming the move and you can go into the folder by clicking on Jump to Folder
Destinations You Won't Be Able to Pick
The folder picker disables destinations that aren't valid, with an explanation:
The folder itself, or any of its subfolders - moving a folder into its own descendant would create a loop, so this isn't allowed.
A destination that would exceed the maximum folder depth
Maximum Depth
All chats → Folder (Level 1) → Subfolder (Level 2)