No, it is not from the spell. It’s from the weapon. Again, the fact that sneak attack damage is magic if the weapon is magic, despite sneak attack not being magic, clearly indicates that when an effect causes an attack to do extra damage, the source of the damage remains the weapon.
Hunter’s Mark does not add damage. Its effect is that attacks against the target do extra damage. Think of it like a force multiplier. Also, Bracers of Archery provide a counter-example to your claim that damage that is the result of a spell, magic item, or magic effect is magical damage. Just like Hunter’s Mark, Bracers of Archery have the effect of causing certain attacks to do extra damage.