This is only relevant for resistances
Some creatures are immune or resistant to damage from nonmagical weapons.
Damage Immunities Bludgeoning, piercing, and slashing from nonmagical weapons
In the case of Unwavering Mark, the extra damage is keyed to the weapon meaning the damage is modified by such resistance.
Contrast this to other sources of extra damage which are not keyed to the weapon:
Kensei Shot: ... any target you hit with a ranged attack using a kensei weapon takes an extra 1d4 damage of the weapon’s type
TheOne interpretation as a result of this difference in wording is that the extra damage of Kensei Shot wouldmay bypass this damage resistance and immunity (those which are specific to weapons) as it is not specifically keyed to the weapon. The Unwavering Mark is likely absent from this interpretation as it specifies the weapon is dealing the damage.