It seems like ranged and melee damage have no effect. Even when using the default skills datapack or adjusting values to be extremely large, things aren't affected.

I may have other mods conflicting, but I think it's unlikely. I can test with a fresh instance if needed.

Line which should increase damage by an absurd 80%:

Skeleton prisoner taking normal bow damage:

Originally this was in a Fabric modpack
I tried again on a fresh install with Forge with no mods except Pufferfish skills and attributes, and now it works.
Either there was a mod conflict or something with fabric, probably the former.