Putting an uncraftable potion in a brewing stand and adding gunpowder plays the brewing animation and spends the gunpowder but doesn't turn the potion into a splash potion. Using a splash potion and adding dragon's breath in the same way doesn't turn it into a lingering potion.
How to reproduce:
Place down a brewing stand and fill in the fuel slot with blaze powder.
Run the command
/give @s minecraft:potion
or/give @s minecraft:splash_potion
Insert the potion you were given into the brewing stand.
Add gunpowder or dragon's breath, respectively, in the ingredient slot.
Wait for the brewing to finish.
Expected result:
The regular / splash potion would turn into a splash / lingering potion.
Observed result:
The regular / splash potion remained a regular / splash potion.
Can confirm. It didn't convert into a lingering potion.