Burn It! increases your intital attack damage once (to each creature)
Burn It! provides a Status bonus to damage. Per the rules, you can only increase the damage of an attack by the highest of each typed bonus, once. Essentially, you do have bonus damage on your bomb and bonus damage on your splash, but they’re not allowed to happen together so you only apply one.
Again like checks, you may also apply circumstance, status, item, and untyped penalties to the damage roll, and again you apply only the greatest penalty of a specific type but apply all untyped penalties together.
Splash is a trait of the attack being used, so it is not it’s own damage instance and does not increase separately from the bomb damage. The status bonus can apply to everyone affected by the splash, because you are still only applying the bonus once.
It increases persistent damage less
The source of persistent damage does not matter. Persistent damage is a Condition that does not adopt traits or features from its origin. It is no longer an alchemical bomb, just persistent fire damage.
In Pathfinder 2e, all fractional numbers are rounded down unless otherwise stated.
You may need to calculate a fraction of a value, like halving damage. Always round down unless otherwise specified. For example, if a spell deals 7 damage and a creature takes half damage from it, that creature takes 3 damage.
- Level 11 bomb (3d8+3 splash and 3 persistent)
- Initial toss 3d8+5 splash (3+11*.25 = 3+ floor(2.75))
- Persistent 4 fire