I was looking for this feature recently and found your addon.
If you don’t mind I updated it for 2.90+ and moved UI to Material Specials.
Credits all yours.
MatSorting.py (3.2 KB)
P.S. if someone curious what is the other options, it’s from MaterialUtilities addon. There is built-in blender but it’s outdated, idn why it still did not get update.