I'm using version StorageDrawers-1.15.2-7.0.2
In the config enableItemConversion = true
I installed the conversion upgrade and a iron storage upgrade into a 2x2 full sized oak storage drawer.

I try to insert different kinds of copper ore by right clicking on the drawer:
Mekanism, Create, Immersive Engineering

All ores have the following tags:
forge:ores/copper
forge:ores

Nothing is converting at all for me. Tried with Tin, Copper, Bronze, Silver and Aluminum.

Just a couple of theories here but It could be related to the blacklist (see issue #108 for an example) as more mods are tagging for anyingot/nugget now as seen in your example by the "forge:ores". In old versions ore dictionary registrations like "ingotAnyMetal" could lead to illegal conversions.
Also 1.15 and 1.16 versions are still in beta so it wouldn't surprise me if the conversion upgrade was broken in the update.