[HediSIX]

The first thing I'd check is that AS is actually installed (as I don't think that stuff migrates from the "standard" version to the Store version). Even if it is installed, you probably have to manually restore all your settings. The other option is to find the userdata folder of your old version and copy that stuff to your Store version. There are a few threads in the Windows forum about where the userdata is stored (if you haven't found it already).

Barring that, I'd need a debug log file.

Sorry, I think I did not explain well
I actually did a fresh install after upgrading my computer, so I formated the drive, reinstalled a fresh windows, and then Kodi from the store. So no migration.
I checked, AS is installed in the addons.
I have sent you the log file. I hope it will help.
The only thing I have noted after a quick read is that it looks like the addon is trying to launch the script from the following location:
C:\Users\myUsername\AppData\Roaming\Kodi\addons\script.artistslideshow\default.py
But this folder does not exist with the UWP version.