How does Battlemage apply the added spell damage.

As per the title, wondering if there's any information or confirmation around how the added damage from main hand weapon works here.

If my weapon does 30 physical and 30 cold damage for example, does it add just 60 spell damage, or does it add 30 physical and 30 cold damage to spells (affected by whatever added damage effectiveness the spell has)?

Cheers

If we look at martyr of innoncence and desintegrator
(If i'm not screwing up the name)

They remove on both of those weapon the flat added damage for spell and replace it by battlemage.

Soo yeah you can kinda expact battle mage to work as flat added damage based on your weapon.

Good part is that you probably don't need to focus that much on stats that you would for a attack build (Crit,as on weapon) and go all in on those flat added damage kinda like wandslinger build.