Soul campfires deal the same damage as regular campfires

The damage dealt by the soul campfire is the same as a regular campfire which is half a heart. For comparison, soul fire itself deals one heart per tick.

How much damage do soul campfires do?

If a player were to walk on a regular campfire, they would take 1 damage; if they walk on a soul campfire, they would take 2 damage. This is negated if they are sneaking or wearing Frost Walker Boots. This is also the same if the player has Fire Resistance.

Do soul campfires do more damage than magma blocks?

This extends into fire as well. Fire, soul fire, both campfires, and magma blocks all deal the same amount of damage to mobs/players.