Can a Zealot Barbarian apply Radiant rage damage?

Rage says

When you make a melee weapon attack using Strength, you gain a bonus to the damage roll that increases as you gain levels as a barbarian, as shown in the Rage Damage column of the Barbarian table.

And a Zealot Barbarian can

At 3rd level, while you’re raging, the first creature you hit on each of your turns with a weapon attack takes extra damage equal to 1d6 + half your barbarian level. The extra damage is necrotic or radiant; you choose the type of damage when you gain this feature.

Can the rage damage be radiant/necrotic, or does it have to be part of the weapon’s damage die? Is Divine Fury part of the weapon damage die?