No Rest for the Wicked: Explanation of Attribute Enchantment Mechanism
If the weapon itself has plague additional damage as shown in the picture, and then enchanted with a plague gemstone, does the damage accumulate?

The answer is yes, it stacks.
Testing with a greatsword against Greatsword Knight, without a gemstone, there is 12-14 plague damage. With the plague gemstone added, the damage increases to 19-23, showing a significant improvement. The specific calculation of how this numerical stacking works is unknown.
Therefore, if you already have a weapon with decent inherent additional attribute damage, it is recommended to enchant it with a corresponding attribute gemstone for higher additional damage values.
If the weapon itself has plague, enchanted with plague, and then used with a potion enchantment, does the damage stack?
The answer is still yes, it stacks.
For the weapon shown in the image, applying a plague oil with plague additional damage directly increased it to over 30, almost equivalent to base damage.
Additional note: Using this weapon with other elemental oils (tested with Frost Scale Oil for ice element), the additional damage will not change to the ice element, nor increase the inherent plague additional damage.