Greater Barghest a Large Creature have the Enlarge (4th) level Innate Spells and the spell say:
The creature is clumsy 1. Its reach increases by 5 feet (or by 10 feet if it started out Tiny), and it gains a +2 status bonus to melee damage. This spell has no effect on a Large or larger creature.
Heightened (4th) The creature instead grows to size Huge. The status bonus to melee damage is +4 and the creature’s reach increases by 10 feet (or 15 feet if the creature started out Tiny). The spell has no effect on a Huge or larger creature.Will this increase it's damage by 4 and add 10ft to it's reach as the spell say or does it already have a +2 status bonus as a large creature?
What will it's Reach be after it´s Enlarged?
I would give only the benefits added as part of heightening, since the spell is written originally with Medium or Small casters in mind. So 5 extra feet of reach and +2 damage. Though I could see the damage increase still being +4.
It doesn't already have a +2 status damage bonus for being large, PF2 has gotten rid of these types of internal prebaked bonus calculations for creatures. Instead the creature just has some given stats, and any status, circumstance, item, or other bonuses would stack on top.