I could buy this too but in the OP world where DF exists and with thing like Nika DF I think it’s likely an other DF rather than a haki form
Yes, They are the Devils found inside DFs
DF Powers & Haki are the same just applied differently
Think of it this way, Every Living Being have their Haki Source inside them which They can learn to tap into
Eating a DF grants you a Second Source of same Energy, except it's not Yours, it's Devil Haki but you can Use it
(It's basically making a Deal with Devil, hence why They are called Devil Fruits)
How do they grant Abilities? Well, it's same Case as Brook
Brook had a Human Body, He lived like a Normal Human, once He died, his Soul got Revived thanks to his DF, but it went back inside his Skeleton only, what happened to this Skeleton? It gained same Functionalities of Brook's Full Original Body even though it's only Bones (Brook literally jokes about this Non-Stop) and even more, it also gained Attributes from Afterlife, something that his Soul only Experienced
In other words, the Soul basically stores All Functionalities it Experienced (Just like Big Mom Homies gaining Eyes & Mouth & Human Attributes thanks to a Soul) and if it connects to a New Host, They gain those same Functionalities regardless of their Bodies (Even if it doesn't have Eyes it can still see for ex)
So DF Users are basically gaining same Functionalities those Devils had in a Previous Life/Body/Experience.
Devils of DFs don't leave this World when their Users Die, meaning They are Banished from Real Afterlife, and yet They always get recycled, that's because They have their own Afterlife where they get sent back everytime They lose their Host
Imu's Cold Room seems to be WG's "Afterlife", that's their Secret, They basically have Davy Jones Locker
Hence the entire Hell References, Devil References, Summoning Circle (Which was also Foreshadowed by Brook when He was sent away by Kuma) ... etc