But jei has recipe:

This craft successfully works with original black dye.

The recipe does not work because Sophisticated Backpacks BackpackDyeRecipe does not use item tags to check for dye, but for dye item specifically: slotStack.getItem() instanceof DyeItem when matching the recipe. But checks the tag when assembling the recipe: slotStack.is(Tags.Items.DYES) - which makes it show up in JEI.

This is on them to fix.