There are actually two folders that you need to backup.
The first has all your mods in it: Program Files (x86) / Electronic Arts / Ultima Online Stygian Abyss / Userinterface
The second folder contains all of your character information and desktop setup: Documents / EA Games / Ultima Online Stygian Abyss / User Data
The User Data folder contains all character info for all Accounts that you've logged into. Open that folder and you can see the individual account names. Open any account name and you can see each shard that account has logged into. Open any shard folder and you can see the individual character desktop files, which contain your desktop setup, hotbars, UI Scaling, macros, etc.
THIS is very handy when setting up a new character, since you can copy, paste and rename the folder to your new character's name to get the exact same desktop, hot bar and macro set up for your new character. I set one character up with the basic hot bars and macros, then copied this file for all my other characters. Now they all have the same "look" but I did have to add new macros and a few hot bars, but this saves a lot of time.