(inspired by this answer)
When you Cast a Spell from your spell slots, if the spell deals damage and doesn’t have a duration, you gain a status bonus to that spell’s damage equal to the spell’s level.
Enervation for example seems to satisfy both criteria. It does not have a duration, and it deals damage (CRB 3rd printing, page 451):
Persistent damage is a condition that causes damage to recur beyond the original effect.
Question 1: does "causes damage" satisfy the "deals damage" criteria?
Question 2: if yes, is it just 4 negative damage when the spell is cast, or is the persistent damage increased by 4?
Best Answer
Dangerous Sorcery does not affect persistent damage
In line with my related answer, causing damage via a Condition is not the same as dealing damage. One is inflicting the target with an effect that has damage associated while the other is the damage being inflicted at the moment by the spell.
If for no other reason, this should fail the Ambiguous Rules' "too good to be true" guidance; Dangerous Sorcery is written such that it should typically only affect each target creature once per spell cast (by disallowing using it on spells that cause damage over a duration). By allowing it to affect persistent damage, you are bypassing this restriction with a number of spells such as enervation and acid arrow. This would increase the feat's power by about 3.3x for those spells, compared to it's expected output.
The result is that enervation gains no benefit from Dangerous Sorcery and acid arrow benefits from it exactly once (assuming a successful attack roll) for the initial damage, just like every other damaging spell.